Transcript Document
Fields
• Model used when force act a distance.
• Quantity / unit measure.
• Direction Too.
Grav field caused by mass g = F g /mass.
N/kg
Electric caused by charge E = F e /q.
N/C
Magnetic Fields B
• • •
caused by moving charges N/C *m/s = Tesla T
What is Magnetism?
Magnetism is the force of attraction or repulsion of a magnetic material due to the excess spin of e-.
Can think of e- circling nucleus are creating bar magnets in magnetic material.
Magnetic Field, B Direction.
Follow compass needle .
Field Strength Strongest near poles. Lines close together.
Earth’s N geographic pole = S mag pole.
Sketching Fields Use arrows to show the direction of compass needle deflection.
Compass needle points away from N and into S mag pole.
Symbols Arrow shows direction in plane of page.
Field into the page X like tail of arrow.
Field out of page … like tip of arrow.
Electric, E & Magnetic, B Fields
Similarities
• • • • •
Directional Field = vector field lines – flux which cannot touch, or bend at sharp angles, intensity is shown by close spacing.
Both attract opposite. Repel like.
Drop off with distance inverse square.
Both Polarize objects.
Differences
•
Magnet feels no force in static E field.
•
Charged particle q, no F in static B field.
•
For B field, direction compass needle points.
•
For E, field direction + test charge would move.
Reading Magnetism Hamper Ch 6.3
• • •
How are magnetic fields sketched?
How are Electric fields sketched?
What is the relationship between charges and magnetic fields?
Moving charges/ currents induce magnetic fields. In specific directions.
•
When a current flows, a magnetic field is generated.
•
*Stationary charges do not generate magnetic fields, but do cause electric fields.
Mag Field Direction around Wire.
Field circles perpendicular to wire.
Wire loop – thumb in current direction. Fingers in B direction.
Solenoid – Loops of wire (can be wrapped around core of iron).
Solenoids have same field as bar magnets.
And Earth
Hand Rule: Find Mag N pole in solenoid.
Fingers in direction of current, thumb points to magnetic N. Pole (see field lines).
Charged particles moving in B fields feel a force!!
Force direction determined by hand rule three.
Direction of mag force on q perpendicular to velocity vector & to field.
For +q place right hand fingers into field, thumb points to v, palm points to mag force.
For –q use left hand or reverse direction of right hand.
Electron in mag field B.
Force is proportional to amount of q on particle.
Magnetic Field Units = Tesla’s Tesla (T) = N C m/s N Am kg m/s 2 A m
Strength/Intensity of Mag Field can be described in terms of force on moving charge q.
F mag = qvB sin
q
B = F mag qv q = charge coulombs v = velocity m/s F = force Newtons B = Tesla
The force on the charge only acts perpendicular to the velocity direction. Charges traveling along field lines feel no force.
Since arises when the mag field and velocity are perpendicular:
•
F
mag
= qvBsin
q
.
•
Where
q
is the angle between the velocity and the magnetic field direction.
• •
When
q
When
q
= zero the force is zero.
= 90 the force is maximum.
Ex 1: A p+ moving east feels a force of 8.8 x 10 -19 N upward due to the Earth’s magnetic field. At this location the field strength is 5.5 x 10 -5 T north. Find the speed of the particle.
F mag = q v B v = F mag qB = 100,000 m/s.
8.8 x 10 -19 N_ (1.6 x 10 -19 C)(5.5 x 10 -5 T )
If there is a component of velocity parallel to the field is unaffected. There is a helical effect.
Magnetic Force on q is F c since it causes curved motion.
Ex 2: An electron moves at right angles in a uniform magnetic field of 3.0 x 10 -3 T. If its speed is 3.0 x 10 5 m/s, what is the radius of the path of the electron?
•
the magnetic force is causing curved motion so it a centripetal force!
.
F
mag
= F
c
.
q
v
B = m
v
2
.
r.
r = mv
2
= mv.
qvB qB
5.7 x 10
-4
m.
Force on current carrying wire.
The current in a wire also feels a force in mag field.
Conventional Current –force direction on wire: fingers into field, thumb in current direction, palm points toward force direction.
Force on wire proportional to direction of field, current, & length of wire in field.
F = BIl sin
q
F = force (N) B = mag field (T) I = current (A) l = length of wire (m)
Ex 3: A wire that is carrying a current of 3.5 A east, has 2.00 m of its length in a uniform field of flux density 5.00 x 10 -7 T directed into the paper.
a) Sketch the wire in the field.
b) Find the magnitude and direction of the force.
F = BIl.
(5.00 x 10 -7 T )(3.5 A )(2.00 m ) = 3.5 x 10 -6 N up.
Ex 4: A 36-m long wire carries 22 A current from east to west. If the maximum magnetic force 4.0 x 10 -2 N directed down, find the magnitude and direction of the magnetic field at this location.
F = BIl B = F/Il. = 4.0x10
-2
N.
(22A)(36m) = 5.0 x 10
-5
T. north.
The current in the wire must be at right angles to the field to feel the force so: F = BI
l
sin q .
Where q is the angle between the wire and the field q
Field & Force Around Parallel Current Carrying Wires
Since currents generate mag fields, two parallel wires will each generate a field that exerts a force on the adjacent wire. The direction of the force depends on the current direction.
Currents in same direction exert attractive forces. Is this real or conventional current?
Hint hand rule for Force - fingers into the B field created by the other wire!
Neg current (real).
Current in opposite directions, create fields with repulsive forces.
By Newton’s 3 rd Law, F 2 = -F 1 .
F 1 F 2 I 1 I 2
The Ampere (A) is a unit of rate of current flow, but is based on the force felt between 2 current-carrying wires.
The Ampere, not the Coulomb, is considered a fundamental unit!! Very weird indeed!
Formal definition of the ampere: “The constant current which will produce an attractive force of 2 × 10 –7 N/m of length between two straight, parallel wires of infinite length and negligible circular cross section placed one meter apart in a vacuum".
These show neg charge flow.
Mag Field interaction Between Current Carrying Wires
Do Now: Sketch the E field between parallel plates.
Sketch the path of an electron beam shot into the field.
Crossed Fields
• • • •
An e- is shot into the magnetic field as below. a. Sketch its path in the field.
b. Suggest a way to use an E field to direct the e- in a straight line.
c. Sketch the electric field that will straighten the e- path.
e d. Derive an equation that expresses the electric field strength E, required to keep an e- of velocity v, moving through a magnetic field B, in a straight line.
End Here
No longer in curriculum
For a straight length of wire the mag field can be expressed as: B =
m
o I 2
p
r
m
o constant find it.
r = dist fr wire m I = current - A B = field strength T
Force between two wires proportional to current in wires: F =
m
o I 1 I 2
l
2
p
r
Ex 4: What is the magnitude & direction of the force btw 5.00 m lengths of wire each carrying 7.5 A of current in the same direction if they are separated by 25.0 cm?
2.25 x 10 -4 N toward each other.
Mag Field Strength around a solenoid:
B = m o NI l N = number turns of wire I = current
l
= length of wire in field m
Hwk Sheet.
Do Holt p 782 with IB ref tables p 781#19, 21, 22, 24, 25, 33, 35, 41, 42