Electrostatics

Lessons from the Lab • Opposites attract, likes repel • Charged objects can attract neutral objects • Attraction is proportional to charge, distance

• Positive charge results from removing electrons from a substance • Negative charge results from adding electrons to a substance • Conducting materials allow charge to flow freely • Insulating materials do not

Properties of “Charge” • Reflects relative number of electrons in a substance • Conserved • Units of Coulombs (C) • An electron has a charge of 1.6 x 10 -19 C of charge

Significant Charge Amounts • When we rub balloons on rabbit hair in the lab, we’re generating 10’s of m C

Which of the following will tell you without a doubt that an object is charged • 1) It attracts another object that has been rubbed with rabbit fur • 2) It repels another object that has been rubbed with fur • 3) It does not attract a neutral object

Three aluminum balls are suspended from the ceiling. All three are charged with various materials. It is found that 1 and 2 repel one another, and 2 and 3 repel one another. From this, we can conclude that: • 1) 1 and 3 carry the same charge • 2) 1 and 3 carry opposite charges • 3) all three carry the same charge • 4) one of the objects carries no charge • 5) we need more experiments to determine charge

Three aluminum balls are suspended from the ceiling. Two of the three are then charged with various materials. It is found that 1 and 2 attract one another, and 2 and 3 repel one another. From this, we can conclude that: • 1) 1 and 3 carry the same charge • 2) 1 and 3 carry opposite charges • 3) all three carry the same charge • 4) one of the objects carries no charge • 5) we need more experiments to determine charge

Which spheres experience the greatest attraction?

Methods of Charging

Charging by Friction • http://phet.colorado.edu/new/simulatio ns/sims.php?sim=John_Travoltage

Charging by Induction • http://phet.colorado.edu/new/simulatio ns/sims.php?sim=Balloons_and_Static_ Electricity

Charge polarization • When the charges in a material arrange themselves in such a way that the material has + and – sides, the material is said to be

polarized

Why does Induction Work?

• Both positive and negative charges are still in a substance • Why is it attracted?

Charging by Contact/Conduction • The physical movement of charge from one object to another

What will happen to two neutral spheres below when you bring a + charged rod close by?

• 1) A and B will become + • 2) A and B will become • 3) The spheres will remain neutral • 4) A will become – and B will become + • 5) A will become + and B will become -

If you want A to remain – and B to remain +, what should you do?

• 1) Remove the rod • 2) Separate the spheres and then remove the rod • 3) Remove the rod, then separate the spheres • 4) Touch the spheres with the rod

Lightning

• We’ve talked about ways to generate attraction and repulsion with charged objects • Just to review, on what does the attraction depend?

• Assuming you’ve got two charged objects, write a basic equation that describes the force of attraction between them (just worry about the magnitude)

Coulomb's Law • Coulomb’s Law gives us a way to calculate the force between two charged objects • F E = kq 1 q 2 /d 2 • k is a constant = 8.99 x 10 9 N m 2 /C 2

Similarities to Gravity • Recall how we calculated the gravitational force between objects: • F G = Gm 1 m 2 /d 2 • G is a constant = 6.67 x 10 -11 • Look familiar?

N m 2 /kg 2

Different Constants • G = 6.67E-11, k = 8.99e9

• What does this tell us about the difference between gravitational forces and electrostatic forces?

• Calculate the electrostatic force between a +6 m C charge and a -5 m C charge, located 2m apart

• Calculate the electrostatic force between a proton in the nucleus of the atom (q = +1.60e-19C) and an electron (q = -1.60e-19C) located in an outer energy level (d = 3e-11m) • Calculate the electron’s acceleration

Levitation • I once heard a person ask, couldn’t you make a person float using charges? • Perhaps • Imagine a person (m = 70kg) gathered -10mC of charge by rubbing herself with rabbit fur • What charge would we need to lift her off the ground?

Examine the configuration below. Which charge would exert the greatest force on the -2 charge? • 1. +8 • 3. +6 2. +4 4. +20

Which list below ranks the charges in order of increasing force on the -2 charge?

• 1. A, B, D, C • 2. A, C, B, D • 3. D, C, B, A • 4. C, A, B, D • 5. D, B, C, A

Which arrow represents the direction of the net force on the -2 charge?

Electric Fields • Like gravity, the electrostatic force is a non-contact force • To conceptually deal with this, we talk about electric fields • This is a region of space surrounding a charged particle that “carries” the electrostatic force

• An electric field tells us the direction of the electrostatic force • It also gives us a sense of the force magnitude

Drawing the Field • Place a positive “test” charge near a charge, or charge configuration • Determine the direction of the net force acting on that positive charge • Draw an arrow in that direction (arrow length represents force magnitude) • Move the charge to another place and repeat

A single positive charge

Which diagram correctly illustrates the field surrounding a negative point charge?

Field Strength • For a single point charge, electric field strength a distance r from the charge: • E = kq/r 2 • Units? • N/C

Calculate the electric field strength, 2m away from a 3mC charge

Force on a charge placed in an E field • F = qE • F = mg

Calculate the force on a 2mC charge, placed in an electric field of strength 500N/C

Calculate the acceleration of an electron (m = 9E-31kg, q = 1.6E-19C), placed in a field of strength 3E-7 N/C

A sphere (m = 2kg, q = 5mC) accelerates at 6m/s/s when placed in an electric field. Find the field strength

• F = q 1 E = q 1 • F = kq 1 q 2 /r 2 (kq 2 /r 2 )

Fields Add • Imagine three charges, each with its own electric field • At point P, E 1 = 20N/C to the right, E 2 10N/C to the left, and E 3 = 15N/C to the right • What is the net field at this point (assume right is +)?

=

Moving Charges • Imagine two positive charges, located 1.0m apart • An outside force moves one charge 50 cm closer to the other • What happens to the system?

• The system gains energy • What type?

• Electric Potential Energy

• What happens if you let the charge go • It moves to a lower energy state • Analogies to gravity?

Connections to E Fields?

• Imagine a positive test charged, placed near a point charge • As the test charge moves with the field lines (ie, in the direction of the arrows), what happens to its EPE?

• A negative test charge?

Field Lines • Tell us the direction in which EPE decreases for a + charge • Tell us the direction in which EPE increases for a - charge

• http://phet.colorado.edu/new/simulatio ns/sims.php?sim=Charges_and_Fields

Which charge configuration has the highest EPE?

• One way to think about the previous question: in which situation do you have to do more work to arrange the charges?

Statics to Dyamics • We’ll focus primarily upon situations where a charge’s EPE changes • We’ve been discussing electro (stationary charges)

statics

• This EPE discussion gets us into the realm of electro charges)

dynamics

(moving

A Sense of Scale • Often times, we talk about groups of charge • To deal with this, we talk about the amount of EPE/total charge • We call this quantity, electric potential

Units?

• Potential = EPE/charge • Units = J/C • 1 J/C = 1 Volt • Electric Potential is often called voltage

Van de Graaff Voltage?

• A Van de Graaff is normally charged to thousands of volts, yet it won’t hurt you if you touch it • Why then, can an outlet (V = 110V) really hurt you?

•Voltage

= EPE/ charge • Voltage =

EPE

/

charge

Connection to E Fields?

• How does test charges electric potential change as it moves through a constnat E field?

• Let’s assume constant field strength to make life easy…

A Mathematical Expression • How does the change in potential relate to the field strength E?

• The distance moved, d?

• D V = Ed • This only works for constant E Fields (we need to use calculus if E is not constant)

Voltage Difference on the Van de Graaf?

• Let’s measure the length of a spark to find D V between the Van de Graaff • Knowing the electric field strength necessary to ionize air (1E6 N/m), we can find D V

Energy Conservation with Charge • A 3mC charge is travels through a potential difference of 110V • How much KE does it gain as it travels through this potential difference?

• In a television, an electron travels through a potential difference of 32,000V • How fast is it traveling when it strikes the television screen?

• When charges are in a region where a potential difference exists, what do they do?

• They move • The movement of charge is called electric current • Units = C/s = Amperes (A)