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AP Physics 11: Magnetism
A.
Name __________________________
Magnetic Properties
1. magnetic Field, B
a. circular field around a straight current wire
into the page 
out of the page 
B
B
I I 
1.



magnitude, B = k'I/r (T—tesla)
a. k’ = o/2 = 4 x 10-7/2 = 2 x 10-7 T•m/A
b. r = distance from wire
2. direction (right hand rule—B)
point thumb in direction of current, I
point hand toward a side of the wire
bend fingers 90o, fingers point in the direction of field, B
b. straight field in the center of a circular current
into the page 
out of the page 
I
I
BB 
magnitude in center of solenoid, B = oI(N/L)
N/L = number of loops (N) per length (L)
2. direction (right hand hitch-hiker rule—B)
make a fist with thumb sticking out
fingers wrap around thumb in direction of current, I
(clockwise or counterclockwise)
thumb points in direction of field, B
c. north and south poles on a permanent magnet
1. magnetic field lines 
1.



2.
2.
no monopoles 
3. Earth's magnetic field 
magnetic force, FB
a. moving charge or
current in B
B
+q
v
FB
1.




I
magnitude
a. FB = qvB
(particle)
b. FB = ILB
(current)
2. direction (flat hand rule—magnetic force)
right hand for + charge (left hand for – charge)
point thumb in direction of v or I
point fingers in direction of B
palm points in the direction of force, FB
3. other direction rules
Wire Loop
Parallel Wires
B
FB-1 = I1L1B2 = k’I1I2L1/r


 contract expand
attract


expand contract
repel

b. FB = Fc  qvB = mv2/r
B


+


q


–
B.
Induced emf, E
1. moving a current loop relative to a magnetic field
generates (induces) an emf, E = B/t
a. number of loops (N): E = N(B/t)
b. magnetic flux,  B = A x B (Wb—Weber)
magnetic field
Flux,  B, is like rain (B)
falling through a loop with
area
area, A
(maximum when AB)
c. change in magnetic flux, B
1. change A or B
a. increase A by rotating the loop from ||  
relative to B (decrease A: ||)
b. increase B by moving a magnet toward the
loop or by increasing current in an electromagnetic (opposite = decrease)
2. induced current
a. I = E/R
b. Lenz's law: the magnetic field that induces
a current and the magnetic field produced
by the current are in the opposite direction
( FB-induced opposes FB-inducing).
c. direction (flip right hand hitch-hiker rule)

make a fist with thumb sticking out pointing in direction
of inducing B

flip your thumb over if Bincreases (Lenz's law)
(don't flip if B decreases)

fingers wrap around thumb in direction of induced
current, I (clockwise or counterclockwise)

summary chart
B
Induced Current, I


+


–

+


–
2. moving a conducting rod through a magnetic field
induces an emf, E = vLB
Steps
start with
substitute A x B for B
substitute Lvt for A
regroup
simplify
3.
4.
Algebra
E = B/t
E = (A x B)/t
E = (Lvt x B)/t
E = Lv(t/t) x B
E = vLB
a. induced current (in rod only), I = E/R = vLB/R
b. direction: use directions above, where increasing
enclosed area = +B
(in the diagram: induced current is    in rod)
conservation of energy and Lenz’s law
a. force needed to move conductor = FB = ILB
b. power needed to move conductor, P = FBvav
c. power generated in the circuit, P = IV
d. P = FBvav = IV (conservation of energy)
transformer, NS/NP = VS/VP = IP/IS
a. device to change voltage
b. examples
1. street to home voltage
2. battery recharger
Practice Problems
1.
2.
3.
A. Magnetic Properties
Determine the direction of B for the moving charges.
Charge
velocity
side
B
a.
+
east
above
b.
+
down
north
c.
+
south
south
d.
+
north
east
e.
+
west
under
f.
–
south
west
g.
–
north
above
h.
–
down
east
Determine the direction of B for the currents.
"Charge"
current
side
a.
+
east
above
b.
+
north
below
c.
+
up
north
d.
+
north
east
e.
+
down
west
f.
+
east
below
g.
+
west
south
11. An alpha particle (q = +2e, m = 6.6 x 10-27kg) enters an 2-T
magnetic field. The radius of its circular path is 10 mm.
Determine the
a. velocity.
B
h.
+
south
above
What is the magnitude and direction of magnetic induction,
B, at a point 5 cm north from a long wire in which the
current is 15 A east?
What is the direction of B at the center of a horizontal wire
loop carrying a clockwise current?
5.
A thin 10-cm-long solenoid has a total of 400 turns of wire
and carries a current of 2.0 A. Calculate the field inside
near the center.
7.
8.
Highlight the correct word.
a. Magnetic field lines are (toward or away from) the N
pole of a permanent magnet.
b. Magnetic field lines are (toward or away from) the N
geographic pole of the earth.
c. The earth's north geographic pole is nearest the
earth's (north or south) magnetic pole.
Determine the direction of FB for the following.
v
B
FB
a.
up
south
b.
south
down
c.
east
down
d.
east
south
e.
west
east
Determine the magnitude and direction of the magnetic
force on a current segment 5 cm long, placed in an upward
magnetic field of strength 1.2 T. The current in the wire is
2500 A to the east.
10. Two long wires, 2 cm apart, carry currents of 100 A in
opposite directions. What is the magnitude and direction
of magnetic force on a 10-cm length of one wire due to the
field of the (very long) other wire?
4.
6.
9.
f.
west
down
Determine the magnitude and direction of the force on an
electron traveling 3 x 106 m/s horizontally to the west in a
vertically upward magnetic field of strength 1.30 T.
b.
kinetic energy.
c.
momentum.
12. The figure shows a cross section of a cathode ray tube.
An electron (m = 9.11 x 10-31 kg, q = -1.6 x 10-19 C) initially
moves east at a speed of 2 x 107 m/s. The electron is
deflected northward by a 6 x l0-4-T magnetic field.
a.
What potential difference is needed to accelerate the
electron to the given velocity?
b.
c.
The direction of the magnetic field is (up or down).
Determine the magnitude of the magnetic force on the
electron.
d.
Determine the radius of curvature of the path followed
by the electron while it is in the magnetic field.
An electric field is later established in the same region as
the magnetic field such that the electron now passes
through the magnetic and electric fields without deflection.
e. Determine magnitude and direction of the electric field.
13. A proton traveling west enters a combined 1000 N/C
electric field and a 0.5 T magnetic field. The proton's path
is undeflected.
a. What is the direction of the magnetic field, if the
electric field is North?
b.
What is the velocity of the proton?
14. Determine the magnitude and direction of the magnetic
field in the following situations.
a. 1 m west of a long wire with a current of 100 A north.
b.
A thin 0.50-m-long solenoid has a total of 10,000 turns
of wire and carries a current of 6.0 A in a
counterclockwise direction.
15. An electron (m = 9.11 x 10-31 kg, q = -1.60 x 10-19 C),
traveling west with a velocity of 1 x 106 m/s enters a
magnetic field, B = 1 x 10-4 T that is directed up. Determine
a. the radius of the circular path.
b.
the direction of the path when viewing from above.
B. Induced emf, E
18. The upward magnetic field through a wire loop changes
from 0 T to 3 T in 0.1 s. The area of the loop is 0.01 m2
and its electrical resistance is 10 .
a. Determine
B
E

I

b. What is the direction of current?
clockwise
19. A horizontal wire loop with area = 1 m2 and resistance = 5 ,
is in a 0.5-T, magnetic field. It rotates 90o in 1 s.
a. Determine
B
16. Wire A carries a 5-A current east. Determine
a. the magnitude and direction of the magnetic field 0.5
m north of wire A.
b.
the magnitude and direction of the magnetic force on a
0.1 m segment of wire B, carrying a 2-A current west
that is 0.5 m to the north of wire A.
E

I

b.
What is the direction of current?
20. A 2-m rod, with an internal resistance of 2 , moves east
through an upward magnetic field (B = 2 T) at 10 m/s.
17. J. J. Thomson's is credited with discovering the electron.
He performed an experiment using the apparatus below to
determine the me/qe ratio for an electron.
a.
Calculate the emf generated by the moving rod
b. Determine the direction of current
in the U-shaped rail and rod
in the rod
c. Calculate the current through the rod.
a.
Initial he adjusted the magnetic and electric fields so
that the "cathode" rays—electrons would strike the
screen at position b.
(1) Determine the direction for the following.
B between the clockwise current loops
d.
Calculate the force needed to move the rod.
FB on the electron beam
e.
Calculate the power needed to move the rod.
E that would keep the electron beam undeflected
(2) What is the velocity of the electron in terms of the
electric field (E) and magnetic field (B)
f.
Calculate the electric power generated in the circuit.
g.
Explain why the answers from parts e and f must be
the same.
b.
The electric field is turned off.
(1) Which path will the electrons follow (a, b or c)?
(2) What is the me/qe ratio in terms of B, E and r, the
radius of the electron's curved path.
21. The metal rails of the U-shaped conductor are 1 m apart. A
rod moves across the rails at 3 m/s in a vertical magnetic
field B = 0.2 T. The resistance is 1 . Determine the
I
FB
P
22. The magnetic field surrounding a horizontal wire loop
changes from 0 T to 5 T (up) in 0.1 s. The radius of the
loop is 0.1 m and its electrical resistance is 10 .
Determine
a. the induced emf.
b.
5.
the magnitude and direction of the induced current as
viewed from above.
What effect does the magnetic force have on the loop?
(A) it expands in size
(B) it contract in size
(C) it rotate about an axis perpendicular to the page
(D) it rotate about an axis in the plane of the page
23. A transformer reduces 120-V ac to 9.0-V dc (a diode
changes ac to dc). The secondary coil contains 30 turns and
the draws 0.4 A. Calculate
a. the number of turns in the primary.
b.
the current in the primary.
c.
the power transformed.
24. A transformer reduces 120-V to 6.0-V. The secondary coil
contains 50 turns and the radio draws 0.25 A. Determine
a. the number of turns in the primary.
b.
c.
A counterclockwise current I in a circular loop of wire is
situated in a magnetic field directed out of the page.
6.
Two parallel wires, each carrying a current I, repel each
other with a force F. If both currents are doubled, the force
of repulsion is
(A) 2F
(B) ½F
(C) 4F
(D) ¼F
7.
Two long, parallel wires, fixed in space, carry currents I1
and I2. The force of attraction has magnitude F. What
currents will give an attractive force of magnitude 4F?
(A) 2I1 and ½I2
(B) I1 and ¼I2
(C) ½I1 and ½I2
(D) 2I1 and 2I2
8.
An electron traveling to the right enters a magnetic field
directed into the page, as a result, the electron changes
direction, but without loss of energy.
the current in the primary.
the power transformed.
Practice Multiple Choice
Briefly explain why the answer is correct in the space provided.
1. An electron is moving south in a downward magnetic field.
What is the direction of the magnetic force on the electron?
(A) west
(B) east
(C) down
(D) north
2.
Which shows the path that the electron follows?
(A) A
(B) B
(C) C
(D) D
What is the direction of the magnetic field north of a wire
carrying a current east?
(A) west
(B) east
(C) down
(D) up
9.
3.
A wire carries a current north in an upward magnetic field.
What is the direction of the magnetic force on the wire?
(A) down
(B) up
(C) east
(D) west
4.
A positively charged particle moves to the right without
deflection through a pair of charged plates. Between the
plates are a uniform electric field, E = 6 N/C and a uniform
magnetic field, B = 2 T, directed as shown.
The speed of the particle is most nearly
(A) 1/3 m/s (B) 2/3 m/s (C) 3 m/s
(D) 12 m/s
A metal spring has its ends attached so that it forms a
circle. It is placed in a uniform magnetic field.
Which of the following will NOT cause a current to be
induced in the spring?
(A) Changing the magnitude of the magnetic field
(B) Increasing the diameter of the circle by stretching the
spring
(C) Rotating the spring about a diameter
(D) Moving the spring perpendicular to the magnetic field
Questions 10-13 A loop of wire has a total resistance of 10 
and an area of 0.01 m2. The wire is initially perpendicular
to a magnetic field of 5 T directed out of the page. The
loop is then rotated 90o so that it is parallel to the magnetic
field.
17. Which is the best estimate of the speed (in m/s) of a proton
in the beam as it moves in the circle?
(A) 10-2
(B) 103
(C) 106
(D) 107
18. A downward magnetic field B is confined to the region of
radius a. The induced emf in the wire loop of radius b is E.
10. Which describes the change in magnetic flux, B?
(A) 0.05 Wb to 0 Wb.
(B) 0 Wb to 0.05 Wb.
(C) 0.5 Wb to 0 Wb.
(D) 0 Wb to 0.5 Wb.
11. If the rotation takes 0.01 s, what is the induced emf, E?
(A) 50 V
(B) 0.5 V
(C) 0.05 V (D) 5 V

12. What is the induced current in the loop?
(A) 50 A
(B) 0.5 A
(C) 0.05 A (D) 5 A
What is the induced emf in the wire loop of radius 2b?
(A) Zero
(B) E/2
(C) E
(D) 2 E
13. What is the direction of the induced current?
(A) out of the paper
(B) into the paper
(C) clockwise
(D) counterclockwise
19. A wire of constant length is moving in a constant magnetic
field, as shown. The wire and the velocity vector are
perpendicular to each other and are both perpendicular to
the field.
14. A rectangular loop of wire is 0.2 m wide with resistance of
20 . One end of the loop is in a downward 2-T magnetic
field. The loop is pulled east at 5 m/s.
x x x x x x x
x x x x x x x
x x x x x x x
0.2 m
5 m/s
x x x x x x x
x x x x x x x
What are the magnitude and direction of the induced
current in the loop?
Magnitude
Direction
(A) 40 A
Clockwise
(B) 40 A
Counterclockwise
(C) 0.1 A
Clockwise
(D) 0.1 A
Counterclockwise
15. In each of the following situations, a bar magnet is aligned
along the axis of a conducting loop. The magnet and the
loop move with the indicated velocities. In which situation
will the bar magnet NOT induce a current in the conducting
loop?
(A)
(B)
(C)
Which graph represents the emf E as a function of v?
(A)
(B)
(C)
(D)
20. Two conducting wire loops move in the directions indicated
at the same velocity, v. The wire carries a current, I, in the
direction indicated.
(D)
Questions 16-17 A proton (q = 10-19 C, m = 10-27 kg) in a magnetic
field (B = 10-1 T) moves in a circle (r = 10-1 m).
16. How much work is done in one complete one revolution?
(A) 0 J
(B) 10-22 J (C) 10-5 J
(D) 102 J
Which of the following is true about the induced electric
currents, if any, in the loops?
Loop 1
Loop 2
(A) No current
No current
(B) No current
Counterclockwise
(C) Clockwise
No current
(D) Clockwise
Clockwise
21. The currents in three parallel wires, X, Y, and Z, each have
magnitude I and are in the directions shown. Wire Y is
closer to wire X than to wire Z.
Practice Free Response
1.
A square loop of wire of side 0.20 m has a resistance of
0.60 . The loop is positioned in a 0.030-T magnetic field.
The field is directed into the page, perpendicular to the
plane of the loop.
x
x
x
x
x
x
x
X
Y
Z
The magnetic force on wire Y is
(A) toward the right
(B) into the page
(C) out of the page
(D) toward the left

Question 22-23 A particle of charge +e and mass m moves with
speed v perpendicular to a magnetic field B directed into
the page. The path of the particle is a circle of radius r.
a.
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
0.20 m
x
x
x
Calculate the magnetic flux B through the loop.
The field strength now increases to 0.20 T in 0.50 s.
b. Calculate the emf E induced in the loop.

22. Which of the following correctly gives the direction of
motion and the equation relating v and r?
Direction
Equation
(A) Clockwise
v = eBr/m
(B) Clockwise
v = (eBr/m)½
(C) Counterclockwise
v = eBr/m
(D) Counterclockwise
v = (eBr/m)½
23. The period of revolution of the particle is
(A) mr/eB
(B) (m/eB)½
(C) 2m/eB
(D) 2(m/eB)½
24. A conducting loop of wire that is initially around
a magnet is pulled away from the magnet
toward the top of the page inducing a current
in the loop. What is the direction of the induced
current and the induced magnetic field?
Induced current Induced magnetic field
(A) clockwise
toward the top
(B) clockwise
toward the bottom
(C) counterclockwise toward the top
(D) counterclockwise toward the bottom
25. A sheet of copper in the plane of the page is connected to
a battery. The copper sheet is in a magnetic field B
directed into the page. P1 and P2 are points at the edges of
the strip.
B
x x x x x
x x x x x
x x Cu
x x x
–
P1 x Sheet
x x P2
E
x x x x x
+
x x x x x
x x x x x
Which of the following statements is true?
(A) P1 is at a higher potential than P2.
(B) P2 is at a higher potential than P1.
(C) P1 and P2 are at equal positive potential.
(D) P1 and P2 are at equal negative potential.
c.
(1) Calculate the current I induced in the loop.

(2) What is the direction of the current in the loop?
2.
The bar of mass M and length D, has a constant current I
flowing through it in the northern direction. The space
between the thin frictionless rails contains a uniform
magnetic field B, perpendicular to the plane of the page.
The magnetic field and rails extend for a distance L. The
magnetic field exerts a constant force on the bar resulting
in its acceleration to the east.
a.
In what direction must the magnetic field B point in
order to create the magnetic force?
Determine the following. Express answers in terms of the
quantities given above.
b. acceleration of the bar.
c.
speed of the bar as it leaves the end of the track.
Determine the following given the values:
B=5T
L = 10 m
I = 200 A
M = 0.5 kg
D = I0 cm
d. speed of the bar as it reaches the end of the track.
e.
the average power to the bar by the electric current.