#### Transcript PHYSICS 2204 (Mr. J Fifield)

**PHYSICS 3204 (Mr. J Fifield)**

**UNIT 3: SECTION 3 Electromagnetic Induction**

**Electromagnetic Induction**

•

**Magnetism In earlier grades you may have made an electromagnet that likely consisted of a nail wrapped with wire. When you connected a battery to the wire, the nail attracted paper clips, staples, and certain coins. **

•

**That the magnet worked only when the battery was connected. This leads to a very interesting and profound observation:**

•

**When electrons are still they have an electric field around them (last section on electrostatics), but when electrons are moving they have an additional field called a magnetic field.**

**Electromagnetic Induction**

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**The electrons undergo two types of motion: spinning and revolving.**

•

**This causes the atom to have a magnetic field around it. That is, it is like a tiny, tiny magnet. The word for such a tiny magnet is dipole, where di-pole means two poles, one is called a north pole and one is called a south pole.**

•

**This magnetic effect is not the same for all materials. The effect would be the same only if the electrons of all materials spinned and revolved in the same way. As you can see from the picture before, a couple of electrons in the same region can have a canceling effect if they rotate in opposite ways. That is, if one rotates clockwise while the other rotates counterclockwise, there will be a canceling effect on the tiny magnetic field . Electromagnetic Induction**

### •

# THE DOMAIN THEORY

**In a substance such as iron which is strongly attracted by a magnet, there must be something about the electron spin and resulting dipoles that are additive in some way. **

•

**The little arrows represent the direction of the magnetic fields of individual dipoles. Note that in small neighbourhoods the dipoles have the same orientation. These small neighbourhoods are called domains . Note from the picture that a domain is also a dipole, that is, each domain has a north and south pole. This piece of iron is u nmagnetized because the magnetic fields of different domains are in random Electromagnetic Induction**

•

**The magnetic fields of the domains of a magnet will be almost perfectly lined up as shown in the next picture.**

•

**The picture also shows that a magnet is a very large dipole.**

**Electromagnetic Induction**

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**The picture below shows what happens to the domains of the piece of iron if it is stroked many times with a magnet. The strong magnetic field of the magnet causes the domains of the piece of iron to line up.**

**Not only do the domains line up, but some domains become larger. **

•

**The piece of iron has become a magnet. We say that it has induced magnetism because the external field of the stroking magnet caused the iron domains to line up.**

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**Note: you should be able to see that any magnet, whether factory made or home made, can have only a certain strength. Once all the domains are lined up or nearly lined up, that's it! It can't become any stronger.**

**Electromagnetic Induction**

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**If the piece of iron is snapped in two, you will have two magnets! Each of the two pieces will have N and S poles. **

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**Since the magnet was created by causing the domains to line up, the piece of iron can be demagnetized by making sure that the domains take up random directions once again. Two ways to do this are 1. By heating the iron 2. By submitting it to some other kind of shock which will cause molecular disturbance.**

**Note: the piece of iron is always a magnetic substance. That is, It always has magnetic characteristics, but it becomes a magnet only when the domains are aligned.**

**Electromagnetic Induction**

# Earth’s Magnetic Field

**English physicist Sir William Gilbert suggested that Earth’s magnetic field is created by the flowing motion of hot liquid metals under Earth’s crust, as shown in Fig. 15.9B. This notion led scientists to a better understanding of the cause of magnetic character at the atomic level (see Section 15.4) The interaction between a compass (a free-spinning permanent magnet) and Earth’s magnetic field has been of great importance for navigators around the world.**

**Electromagnetic Induction**

**By examining how solid iron from lava flow is magnetized, Geologists have determined that the direction of Earth’s magnetic field has changed in the past. Layers of Earth’s crust from different eras show that the domain directions are in opposite directions. Earth’s North Pole is really a magnetic south because the north end of a compass points to it. The magnetic field also varies in strength over the earth's surface. It is strongest at the poles and weakest at the equator.**

**Electromagnetic Induction**

**Magnetic Properties**

• •

**Substances that are attracted Paramagnetic substances are attracted by a magnet. In such substances the spin of one electron is not cancelled by another. Paramagnetic substances that are strongly attracted, are called ferromagnetic. Some platinum.**

**ferromagnetic substances are iron, cobalt and nickel. Other paramagnetic substances that are attracted to a lesser degree are oxygen, aluminum and **

• •

**Subtances that are repelled In some substances electrons are paired in such a way that the spin of one cancels the spin of another. Such substances are weakly repelled by a magnet and are called diamagnetic . Examples are bismuth, zinc, silver and carbon.**

**Electromagnetic Induction**

**Magnetic Fields**

**Using a compass it is possible to map a magnetic field as shown. The direction of a magnetic field at a point within the field is the direction that a compass points when place at that location--in other words magnetic lines of force start at the north pole and end at the south pole. Electromagnetic Induction**

**The Law of Magnetic Forces**

*Similar *magnetic poles

*Similar*magnetic poles

**(north and north or south and south) repel one another with a force, even at a distance apart.**

**Electromagnetic Induction**

### •

*Dissimilar *

### poles (north and south or south and north)

*attract *

### one another with a force, even at a distance apart.

**Electromagnetic Induction**

**Activity**

### • Read Text Pages: 627 - 632 • Extra Practice Questions: In your textbook: • on p. 638--do #1, #2 a, d, c, f • on p. 663--do #6 - #8

**Electromagnetic Induction**

# MAPPING FIELD LINES

**Recall that to map an electric or gravitational field, we use a test charge or test mass, respectively. To map a magnetic field, a compass is used It is used to detect the presence of a magnetic field by applying the law of magnetic forces. The north end of the compass is repelled by the north pole of any magnet creating the field.**

**Electromagnetic Induction**

**The test compass maps the field lines around a simple bar magnet by rotating its dipole to indicate the direction of force that its North end experiences in the magnetic field at that particular point in space. Magnetic field lines are drawn tangent to the compass needle at any point. The number of lines per unit area is proportional to the magnitude of the magnetic field. The direction of the magnetic field is defined as the direction in which the north pole of a test magnet (compass) would point when placed at that location.**

**Electromagnetic Induction**

**Using iron filings is equivalent to using many tiny compasses with undefined poles. Notice how the magnet is a dipole because each field line begins at one pole and flows to the corresponding point on the opposite pole. The law of magnetic forces dictates the convention that field lines flow from the north pole to the south pole of the field-creating magnet.**

**Electromagnetic Induction**

## The Magnetic Field Around a Straight Conductor

**Demonstration Question: **

**What does this indicate?**

**Electromagnetic Induction**

## The Magnetic Field Around a Straight Conductor

**We have already said that when electrons move they Have a field called a magnetic field. Oersted, Hans (1777-1851), a Danish physicist, in 1819, discovered the deflection of a compass needle while near a current-carrying wire performing a demonstration for his students. **

**This discovery of a connection between electricity and magnetism rocked the scientific community.**

**Electromagnetic Induction**

**The picture below shows the magnetic field around a straight piece of wire with the current traveling from left to right. The magnetic field lines form concentric circles around the wire. The direction of the magnetic field is perpendicular to the wire and is in the direction the fingers of your left hand would curl if you wrapped them around the wire with your thumb in the direction of the current. ( Left-hand Rule) Electromagnetic Induction**

•

**Imagine that the wire is bent so the back end is on the bottom with the current going into the screen (the X represents the back end of the current arrow), and the front end is on the top with the current coming out of the screen (the dot represents the tip of the current arrow). **

•

**Again use left-hand rule to confirm that the magnetic field is in the proper direction. Note the region where the magnetic field lines are in the same direction.**

**Electromagnetic Induction**

**Cautionary Note You are going to meet several left-hand rules. It is extremely important to remember that left-hand rules do not work for moving positive charges (only for moving negative charges). Equally important, if you do physics in college or university, you will likely be using conventional current (flowing from + to - as pointed out in Section 02, Lesson 01). Left hand rules do not work for conventional current.**

**Electromagnetic Induction**

**Now imagine that you have wrapped it around a cardboard centre like the one found in the centre of a roll of toilet paper. The result will be something like the picture (right).**

**Use your imagination again, and visualize what you would "see" if the coil were sawed down the middle: If you discard the half of the coil nearest you, will be left with something like the picture below. On the top of the coil the current is coming out of the screen , and on the bottom of the coil the current is going into the screen. The magnetic field is shown for each turn of wire.**

**Electromagnetic Induction**

**Look more closely at the way the fields of each turn add together.**

**Inside the coil all the little fields add up to the left. On the outside of the coil all the fields add up to the right. The end result can pictured as follows. If the coil is long and has many turns it is called a solenoid .**

**The magnetic field around a soleinoid is identical to that of a bar magnet Electromagnetic Induction**

## Magnetic Fields around Current Carrying Conductors (coils)

**The direction of the field may be determined by the ‘ Left hand Rule for solenoids”. Electromagnetic Induction**

**Note The location of the N-pole depends on more than the current direction. It also depends on the way the turns are wound. Look at the next coils carefully: Electromagnetic Induction**

## The strength of an electromagnet

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**In elementary school, you very probably made an electromagnet by wrapping wire around a nail or an iron bolt. **

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**The magnetic field around such an electromagnet depends on the (i) direction of the current and (ii) the direction in which coil is wound Electromagnetic Induction**

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## Factors that affect the strength are

:

**1. the size of the current -the bigger the current, the stronger the field **

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**2. the number of turns in the coil -the more tightly wound the coil is, the stronger will be the field **

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**3. the size of the coil -the smaller the diameter, the stronger the field **

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**4. the type of core inside the coil -an electromagnet wrapped around a ferromagnetic core will be much stronger than one wrapped around a cardboard coil. The reason is that the domains within the ferromagnetic core line up due to the magnetic field passing through the centre of the coil. Electromagnetic Induction**

•

**There is a term that accounts for the change in the strength of an electromagnetic according to the type of material that comprises the core. The term is magnetic permeability, and it is represented by the **

**Greek letter mu (**

μ

**). **

•

**The relative magnetic permeability of a substance is a ratio of the strength of the magnet when the core is made of that substance to the strength when their is no core at all. **

•

**Ferromagnetic substances have a high permeability. You can find the magnetic permeability of some familiar substances in Table 15.3 on p. 637 of your textbook. Electromagnetic Induction**

# The Motor Principle

•

**Electric motors may look complicated when you look at them, but the underlying principle is as simple as this: **

**if two magnetic fields are in the same vicinity, they will act on each other.**

**You already know this is true for two permanent magnets depending on how they are brought near, their magnetic fields either attract each other, or repel each other. That is, one magnet can make the other move. And that is the basic operation of a motor: **

**two magnetic fields make the inside part of the motor move.**

**Electromagnetic Induction**

**Only two magnetic fields are needed to make a motor. The are two options: **

**1. the permanent field around a permanent magnet, 2. the field that we can start up and shut off around a conductor. **

**Electromagnetic Induction**

# Simple motor

**In the first picture you can see only one magnetic field. There is no sign of a circular field yet. This is because the switch is opened, there is no current flowing, and no circular magnetic field around the straight conductor which is hanging like a motionless swing.**

**Electromagnetic Induction**

**When the switch is closed, the current flows and a circular pink magnetic field is created around the conductor according to left- hand rule #1. Look at the black field and the pink field to the left of the conductor. The black arrows and the pink arrows are in the same direction. This means the two fields are repelling each other to the left of the conductor. Look at the black field and pink field to the right of the conductor. The black arrows and the pink arrows are in opposite directions. Therefore in this region the fields are attracting each other. The end result is that the conductor is kicked to the right. We have made motion out of electricity and magnetism. We have created a motor!!**

**Electromagnetic Induction**

**The area where the action takes place is shown in a blow-up below.**

**Study the picture until you can see the fields in the same direction to the left of the conductor (repelling); and the fields in opposite directions to the right of the conductor (attraction). The conductor will be forced to the right.**

**Electromagnetic Induction**

**left-hand rule #3 . When a straight conductor is in a magnetic field and is carrying a current, it will experience a force. You can find the direction of that force like this: point the fingers of your left hand in the direction of the external (permanent) field. Point your thumb in the direction of the current. Then your palm points in the direction of the force on the conductor.**

**Electromagnetic Induction**

**The picture below shows the action of a straight current-carrying conductor placed between the North and South poles of two bar magnets. Using left- hand rule #3 you may predict the direction of the force on the wire when (i) the current goes into the screen, (ii) the current comes out of the screen Electromagnetic Induction**

**If you have ever taken a motor apart, you know that the inside piece that rotates consists of many, many turns of wire. This is too complicated to draw here, but we can show why the "rotor" rotates by looking at just one of the turns of wire. **

g

**" and "h" are brushes. "e" and "f" make up a split-ring commutator with a half-ring attached to each end of the loop. The brushes allow the current to pass into and out of the loop via the split rings.**

**Electromagnetic Induction**

**In the picture the loop is more or less horizontal and a current is flowing through the loop. We have seen that the loop will rotate because of the interaction of the permanent field and the induced circular field.**

**question What can you say about the current in the loop when the loop has rotated ¼ of a complete rotation from its present position? (Look at the picture carefully).**

**answer When the loop rotates 90o from its present position, the gaps between the rings will be touching the brushes. No current will flow for that split, split, split second.**

**Electromagnetic Induction**

**Question Will the loop stop after making ¼ turn? Answer No!! Inertia will keep it moving.**

**Question Is the inertia required to make the loop rotate very far?**

**Answer Hardly anywhere.**

**Question How come?**

**Answer Because almost immediately split ring "e" comes in contact brush "h", and split ring "f" comes in contact with brush "g". When that happens, the current flows in the loop once more.**

**Electromagnetic Induction**

**Below shows the "end-on" view of the same loop. You are looking directly into the screen. Electromagnetic Induction**

**The Motor Principle**

**Determining the size of the force on the straight conductor **

**How may we increase the size of the (green) force on the straight conductor? That is, how can we make our motor more powerful? There are FOUR ways: Electromagnetic Induction**

**There are FOUR ways: 1. We can **

**increase the size of the permanent magnets**

**, which will in turn increase the strength of the permanent magnetic field (the vertical black lines). The symbol for magnetic field strength is B. The larger B is, the larger the force on the conductor will be, **

**or F α B.**

**2. We can increase the size of the circular field that is induced by the current in the conductor. This may be done by **

**increasing the current (I) in the conductor**

**. The larger I is, the larger the force on the conductor will be, or **

**Fα I**

.

**Electromagnetic Induction**

**3. If the length (L) of the conductor is increased , the fields that interact are also effectively increased. The longer the conductor, the more circular field there will be to interact with the permanent field, therefore Fα L.**

**4. The force F is directly proportional to the sine of the angle that the conductor makes with the permanent field: F **

α

**sin .**

**Electromagnetic Induction**

**Finally, we put all of the proportions together to get **

**F **

α

**BIL sin .**

**The force (F) exerted on a straight current-carrying conductor in a magnetic field of strength B is directly proportional to the product of the strength of the field, the current (I) in the conductor, the length (L) of the conductor, and the sine of the angle that the conductor makes with the field.**

**Choosing k as a proportionality constant permits the following equation: F = k BIL sin , Now solve the equation for B gives: Electromagnetic Induction**

**B has the unit Telsa in honour of engineer, Nicola Tesla (1856-1943): 1 tesla (T) is the magnitude of the magnetic field strength (B) that causes a conductor of length 1.0 m to experience a force of 1.0 N when when the conductor is carrying a current of 1.0 ampere and is perpendicular to the magnetic field Electromagnetic Induction**

**Practice exercise 1 Calculate the magnitude of the force on a 2.1 m wire that is carrying a current of 5.0 A perpendicular to a magnetic field of strength 1.4 x 10 -4 T.**

**Solution L = 2.1 m I = 5.0 A B = 1.4 x 10 -4 F = ?**

**T = 90 F = BIL sin = 1.4 x 10 -4 T x 5.0 A x 2.1 m x sin 90 = 1.47 x 10 -3 = 1.5 x 10 -3 N Working out the units: Electromagnetic Induction**

**Practice exercise 2 The wire (and current) in practice exercise 1 is running from east to west. The magnetic field direction is from north to south. In which direction will the force be exerted on the conductor?**

**Solution (method 1) Left-hand rule #1 is used to draw the circular field around the conductor. The permanent (black) field and the pink circular field are in the same direction above the conductor, but in opposite directions below the conductor. Therefore, above the conductor the fields repel each other, and below the conductor the fields attract each other. The net force on the conductor is therefore downward!**

**Method 2 Simply use The LHR #3 Electromagnetic Induction**

**Practice exercise 3 Determine by what factor the force diminishes if a conductor changes its orientation from being perpendicular to the magnetic field to a new position that makes an angle of 45 o with the field.**

**Solution Since the only thing that changed is the angle, we write L2 = L1 I2 = I2 1 = 90 2 = 45 B1 = B2 Determine F2/F1 : When the conductor is at an angle of 45 the field.**

**o with the field, the force on the conductor is less than 75% of the force when the conductor is perpendicular to Electromagnetic Induction**

**Practice exercise 4 A 3.0 m wire has a linear density of 0.020 kg/m. The wire is sitting in a magnetic field of strength 3.5 x 10 -3 T and the wire is perpendicular to the lines of force. How large a current would be required in order for the wire to be suspended against gravity in the magnetic field?**

**Solution We know that gravity is pulling down with a force F =mg, and, if the wire is to be suspended, the magnetic force (F= BIL sin) must be pushing upward with an equal and opposite force. In other words, BIL sin = mg.**

**L = 3.0 m θ = 90 o B = 3.5 x 10-3 T m = 3.0 m x 0.02 kg/m = 0.06 kg g = 9.8 N/kg I = ?**

**Make the substitutions: Electromagnetic Induction**

**The Galvanometer--an Application of the Motor Principle A galvanometer is an instrument used to measure very tiny currents. It consists of a small coil of wire that can rotate in the magnetic field of a permanent magnet. In the picture. Use left-hand rule #2 to confirm that for the given current, the N and S poles of the coil are shown properly. The poles of the coil are attracted to the poles of the permanent magnet and the coil turns so that the pointer moves to the right of the zero reading. When the current is turned off, a restoring spring (not shown) pulls the pointer back to zero. If the current source is reconnected in reverse, then the N and S poles of the coil switch ends, and the pointer swings to the left of the zero position Electromagnetic Induction**

**Activity**

•

**Read Text Pages: 633 - 642**

• • • • • •

**Extra Practice Questions: In your textbook: In your textbook: p. 650--do #1, #2.**

**p. 663--do #10, #11.**

**p. 664--do #25, #26 p. 665--do #37 Electromagnetic Induction**

**A little Review...**

**Remember, Hans Christian Oersted discovered that the magnetic field around a conductor appears as shown.**

**The larger the current the stronger the magnetic field, or B **

α

**I.**

**Also, The larger the distance the weaker the field. This is an inverse relationship, written as . Combing the two we get André Marie Ampere was interested in extending Oersted's discovery to a more general situation where the conductor is not necessarily a straight one, and the path around the conductor is not a nice circle. The latter of these two conditions is shown in the next picture.**

**Next slide....**

**Electromagnetic Induction**

**In the second part of the picture the path is broken into tiny segments **

Δ

**L and each tiny path segment has a small parallel component of the magnetic field strength B associated with it.**

**Ampere was able to show that the sum of the products of was directly proportional to the current I flowing through the closed path. In other words, the larger the current, the bigger the sum of the little products. The proportionality can be written as an equation when a constant of proportionality is inserted. Ampere was able to show that the constant was a very special one: it was !! Recall that is the magnetic permeability of the substance in which the field is located . The mathematical form of Ampere's Law is therefore Electromagnetic Induction**

**The Magnetic Field (B) around a Straight Current Carrying Conductor Now we will apply Ampere's general statement to Oersted's special case where the pattern of the magnetic field is a perfect circle around a straight conductor.**

**Since everywhere on the uniform circular path, and B can be factored out to give Next….. Electromagnetic Induction**

**Note that the difference is in the presentation of the proportionality constant. As derived from Ampere's Law, k has a very special characteristic that includes the magnetic permeability (**

μ

**) of the substance in which the field is located. If the field is in free space, the **

μ

**written as **

μ

**o where **

μ

**o = 4 x 10 - 7 T·m/A is . Air can be considered to be free space.**

**The expression is attributed to Jean-Baptiste Biot (1774 1862) and is called Biot's Law.**

**The law states that the magnetic field strength (B) is directly proportional to the current in a straight conductor, and inversely proportional to the perpendicular distance (r) away from the conductor, with the constant of proportionality being **

μ

**/**

π

**2 Electromagnetic Induction**

**Practice exercise 1 Find the magnetic field strength (B) in air 7.0 mm away from a straight conductor in which there is a current of 2.0 A.**

**Solution r = 7.0 mm = 7.0 x 10 -3 I = 2.0 A**

μ

**o = 4 x 10 -7 B = ?**

**m T·m/A (air) Electromagnetic Induction**

**Practice exercise 2 When a potential difference of 12.0 V is applied to a straight conductor, the magnetic field strength (B) 2.0 cm from the conductor is 3.0 x 10 -5 T. What is the resistance of the conductor?**

**Solution In Biot's Law there is no mention of voltage and resistance. But there is mention of current. So, if we can find the current, it will be easy to compute the resistance (from Ohm's Law).**

**V = 12.0 V B = 3.0 x 10 -5 o = 4**

π

**x 10 -7 T T·m/A (air) r = 2.0 cm = 2.0 x 10 -2 m R = ? I = ? (we must determine I before we can compute R) Electromagnetic Induction**

**Use Biot's Law to determine I. Use Ohm's Law to determine the resistance of the conductor.**

**Solving Biot's Law for I gives Then applying Ohm's Law: R = V/I = 12.0 V / 3 A = 4.0 .**

**Electromagnetic Induction**

**Practice exercise 3 Two parallel wires each carry 5.0 A of current in opposite directions. What is the magnetic field strength midway between the wires if the wires are 10 cm apart?**

**Solution I 1 = I 2 r 1 = r 2**

μ

**o = 4**

π

**= I = 5 A = r = 5.0 cm = 5.0 x 10 x 10 -7 T·m/A (air) 2 m B 1 = ? B 2 = ?**

**Electromagnetic Induction**

**Because of the identical givens, it is easy to see that B 1 Moreover, since B 1 and B 2 = B 2 . are in the same direction, the total magnetic field strength midway between the wires will be B 1 + B 2 .**

**The magnetic field strength midway between the wires is B 1 + B 2 = 2 x 10 -5 T + 2 x 10 -5 T = 4 x 10 -5 T.**

**Electromagnetic Induction**

**Activity**

• • • • •

**Extra Practice Questions: In your textbook: In your textbook: p. 663--do #17, #18 p. 664--do #22. (To do part b, assume that the wires are 2.0 cm apart) Electromagnetic Induction**

**Magnetic Force on Moving Charges**

**Review: you learned that 1 ampere of current represented a flow of 1 coulomb of charge in one second; you also found out that 1 coulomb of charge was comprised of more than 6 billion electrons! A new Definition: Using Magnetic Fields to define one Ampere Two current carrying wires below each carries 1.0 A of current. Also, the wires are 1.0 m long and are also 1.0 m apart. Remember in air, the magnetic permeability is **

μ

**o = 4**

π

**x 10 -7 T·m/A.**

**Notice: I 1 = I 2 = 1.0 A, therefore B 1 = B 2 . Also the magnitudes of F 2 on 1 and F 1 on 2 would be equal even if the currents were different (due to Newton's Third Law).**

**In the area between the wires, the fields are in the same direction (out of the screen) and therefore repel each other**

.

**Electromagnetic Induction**

**.**

**Notice: I 1 = I 2 = 1.0 A, therefore B 1 = B 2 . Also the magnitudes of F 2 on 1 and F 1 on 2 would be equal even if the currents were different (due to Newton's Third Law).**

**In the area between the wires, the fields are in the same direction (out of the screen) and therefore repel each other**

.

**Electromagnetic Induction**

**Now compute the magnitude of the green repelling force (F).**

**the permanent field. Let B 1 be Remember, according to the motor principle, wire #2 will experience a force because it is carrying a current and lying in the magnetic field B 1 . That force is F = F 1 on 2 = B 1 I 2 L 2 sin **

θ

**, where sin**

θ

**= 1 because the downward current in wire #2 is perpendicular to the horizontal "circles" of B 1 . This leaves us with F = B 1 I 2 L 2 .**

**Notice that the F is the force that wire #1 is exerting on wire #2. The right-hand side of the expression tells us this as well. There you will see that the magnetic field of wire #1 (that's B 1 ) is acting on the current and length of wire #2 (that's I 2 and L 2 ).**

**Electromagnetic Induction**

**The expression F = B 1 I 2 we know I 2 and L 2 L 2 is not of much use because even though , we do not have the equipment to measure B 1 . This is where Biot comes in. Remember from earlier that the following expression can be written for wire #1: where r is the distance from wire #1 to wire #2 and o is the magnetic permeability of free space (in this case air). Substituting Biot's Law into F = B 1 I 2 L 2 gives At last we can calculate the magnetic force that two 1.0 m wires exert on each other when they each carry a current of 1.0 A and are 1.0 m apart. Electromagnetic Induction**

**And finally, a more satisfying definition of one ampere of current:**

*One ampere (1 A) is the current flowing through two parallel wires placed one meter apart in air when the wires exert a force of 2 x 10 -7 N/m on each other for each metre of their length.*

**Electromagnetic Induction**

**Exercise 1 Two wires are lying parallel to each other and 13 mm apart. One of the wires is carrying a current of 3.5 A and the force between the wires is 2.5 x 10 -4 N/m. What is the current in the other wire? Solution r = 13 mm = 13 x 10 -3 m I 1 = 3.5 A F = 2.5 x 10 -4 N/m **

θ

**= 90 o**

μ

**o = 4**

π

**x 10 -7 T·m/A L 1 = L2 = 1.0 m (The lengths are not given. However, the force is given as N/m, which dictates that the lengths must be one metre.) I 2 = ?**

**The force on one wire by the other is F = BIL sin**

θ

**where the B is around one wire and the I and the L refer to the other. Also sin 90 o 1, so more specifically, F = B 1 I 2 L 2 .**

**= Next……..**

**Electromagnetic Induction**

**The other thing to remember is that B 1 substituting for B 1 into F = B 1 I 2 L 2 = gives (**

μ

**o /2**

π

**) I 1 and A similar exercise can be found on p. 647 of your textbook where r is the unknown.**

**Electromagnetic Induction**

**The other thing to remember is that B 1 substituting for B 1 into F = B 1 I 2 L 2 gives = (**

μ

**o /2**

π

**) I 1 and A similar exercise can be found on p. 647 of your textbook where r is the unknown Electromagnetic Induction**

## The Magnetic Force on a Single Moving Charge

**We have seen that the force on a current-carrying conductor as it sits an external magnetic field is F = BIL sin**

θ

**. The key is current-carrying. If there were no current, there would be no force on the conductor.**

**So, the force is really exerted on the current. The conductor just provides a path for the current. If a stream of electrons were shot through a magnetic field the force on the stream would still be F = BIL sin**

θ

**, where, in this case, L would be the length of the stream that falls within the magnetic field.**

**Next we are going to determine the force on a single charged particle . Instead of a current of electrons passing through a magnetic field, imagine a single electron (charge q) being fired into the field.**

**single charge could be a proton, neutron or ion. In fact the Continue Next slide...**

**Electromagnetic Induction**

**Think: The charge q is traveling at a speed v and takes a time of t to travel a distance L . Since distance = speed x time, we can write L = vt.**

**If there is a stream of electrons, and there are stream, the total charge will be Q = nq.**

**n charges of size q in the Remember, that current is the rate of flow of charge. That is So now Use L = vt and I = nq/t to re-write F = BIL sinθ .**

**Electromagnetic Induction**

**Summing up, The magnetic force on an individual moving charge is given by the equation F = Bqv sinθ where B is the magnetic field strength in tesla (T), q is the magnitude of the charge in coulombs (C) that is moving at a velocity v in m/s, and is the angle between To determine the direction of the force apply left-hand rule #3: point your fingers in the direction of the magnetic field, your thumb in the direction that the charge is moving, then the palm of your hand points in the direction of the force on the charge.**

**Electromagnetic Induction**

**Practice exercise 2 A magnetic field of 44.0 T is directed into the screen. A particle with a negative charge of 2.0 x 10 -18 C is shot into the field from the right, making an angle of 90 o at 5.4 x 10 7 with the field lines. If the particle is moving m/s, what magnetic force doe it experience?**

**Solution B = 44.0 T q = 2.0 x 10 -18 C v = 5.4 x 10 7 m/s = 90 o F = ?**

**F = Bqv sin θ = 44.0 T x 2.0 x 10 -18 = 4.8 x 10 -9 N C x 5.4 x 10 7 m/s Sin 90 o The magnitude of the force is 4.8 x 10 -9 N. Use left hand rule #3 to determine the direction in which the particle is deflected. This means the particle is deflected towards the top of the screen. Electromagnetic Induction**

**Moving Charges Circular motion**

**A particle moving at constant speed in a uniform magnetic field where the field is perpendicular to the particles velocity will trace a circular path .**

**This means that the magnetic force will provide a centripetal force to keep the particle in circular motion.**

**Where: r: radius of curvature of particle, meters (m) v: velocity of particle (m/s) B: Magnetic Field Strength Tesla (T) q: Charge on the particle (C Electromagnetic Induction**

**Practice Exercise 1 An electron travelling at 7.7 x 10 6 m/s enters into a uniform magnetic field at a right angle. It is deflected in a circular path with a radius of 3.5 x 10 -2 m. What is the magnitude of the magnetic field it experiences? (PUBLIC EXAM, JUNE 2005) Electromagnetic Induction**

**Activity**

**Extra Practice Questions: In your textbook:**

• • • • • • •

**In your textbook: p. 652--do #6--#8. When doing #8, substitute your right hand in left-hand rule #3 because a proton has a positive charge.**

**p. 663--do #12, #14 p. 665--do #31, Electromagnetic Induction**

**Assignment Do research and prepare a written report on the applications of the motor principle that are found in Section 15.6 of your text (magnetohydrodynamics and the mass spectrometer) it would be helpful to know the following: Review: - when a charge q is in an electric field E , the force that the electric field exerts on the charge is F = qE . If the charge is an electron, then the expression can be written as F = eE . - when a charge q is moving perpendicular to a magnetic field B, the force that the magnetic field exerts on the charge is F=qvB (because sin =1.**

**- objects of mass m moving in a circular path are experiencing a centripetal force which is expressed as F = mv 2 /r. Electromagnetic Induction**

**Introducing Faraday’s Law**

**Michael Faraday discovered an exactly opposite phenomenon to Oersted’s principle .**

**Faraday's Law : when a magnetic field moves near a conductor it makes any free charge in the conductor move. --that is, a changing magnetic field creates a current. A magnetic field can change in two ways: 1. It can move physically. ( i) if you move a bar magnet back and forth, then its magnetic field also moves back and forth and (ii) the magnetic field can remain stationary while the conductor itself is moved back and forth.**

**2. It can also change by having its intensity or strength increased or decreased. (ie. By changing the current through the coil).**

**Electromagnetic Induction**

## Faraday's Discovery - illustrations

**The relative motion of the conductor and the external magnetic field has induced a current in the conductor- Faraday's Law.**

**Important: either the conductor must move , or the magnetic field must move, or the magnetic field must change in intensity in order that for the current to be induced.**

**Electromagnetic Induction**

**Here the path of the representative electron (the red arrow) is now such that the blue circular magnetic field is perpendicular to the black permanent field. Because the fields are perpendicular, they cannot interact. Therefore, the electron feels no force due to the external field, and there will be no induced current.**

**If the conductor is pulled through at some angle, then there will be an induced current greater than zero but less than the maximum that results when the conductor cuts the field lines at 90 o Electromagnetic Induction**

**Using Faraday's Discovery to produce Alternating Current (AC)**

**A dry cell or battery is a source of electric current that travels only in one direction. It is called direct current ( DC ) Alternating current does not travel in the same direction all the time. Neither does the current have a constant magnitude. **

A

**simple way to produce AC , can be seen in Fig 16.2 on p. 670.**

**Also shown right.**

**As the magnet is pushed in and pulled from the coil, the galvanometer needle will show that the current reaches a maximum in one direction, then goes to zero and reaches a maximum in the other direction. This illustrates that there is an alternating current in the coil circuit.**

**Electromagnetic Induction**

**Electromagnetic Induction**

**Faraday's Iron Ring Apparatus**

**The operation of the iron ring is just an extension of the picture before where the magnet is moving in and out of the coil.**

**The primary coil has a current (of if you like, voltage) source, and the secondary coil does not. When the switch is closed a current begins to flow and in a split second reaches a certain maximum amount. In the short time that the current is "growing", a magnetic field will "bloom" or expand around the primary coil. The primary coil becomes, an electromagnet. As the primary field expands, its lines of force will cut through the turns of the secondary coil. According to Faraday's discovery, as the magnetic field cuts through the secondary coil, a current will be induced in the secondary coil and the galvanometer needle will move.**

**Electromagnetic Induction**

**Remember a current is induced only as long as the magnetic field is changing, that takes only a split, split, split second for the current in the primary coil to reach some maximum reading. So, after the split second, the galvanometer drops back to zero.**

**Now when the switch in the primary coil is opened, the current dies away and therefore the magnetic field collapses. The force lines are once again moving through the secondary coil, but in the opposite direction. A current will be induced again, but this time in the opposite direction. The galvanometer needle move opposite to the original deflection when the switch was closed. This deflection again lasts for the split second that it takes the current to drop to zero. After that, there is no field around the primary.**

**If the switch is repeatedly opened and closed, the galvanometer needle will indicate an alternating current, first one way, and then the other. Electromagnetic Induction**

**Activity**

• • • • •

**Read textbook page 670 -671 Extra Practice Questions: In your textbook: In your textbook:**

**p. 671--do #1-#3 p. 686--do #1--#3, #6, #9**

**Electromagnetic Induction**

**Electromagnetic Induction**