Physics 11: Magnetism
A.
Name __________________________
Magnetic force and field (20-1 to 20-7)
1. magnetic force, FB
moving charge or current in a magnetic field B
produces a magnetic force if v or I is  to B
B
B
I
v
+q
L
FB
FB
magnitude
FB = qvB
FB = ILB
(particle)
(current)
b. FB is always  to v  FB = Fc  qvB = mv2/r
c. direction (flat hand rule—magnetic force)
right hand for + charge or I (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
o particle turns to form a circular path with palm
toward the center of the circle
o current segment moves in direction of FB
o force on a current loop causes the loop to
contract (palm inward) or expand (palm outward)
sources of magnetic Field B
a. circular field around a straight current wire
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: point your right thumb in the direction
of I, your fingers wrap in the direction of B
into the page
out of the page
B
B
a.




2.
  
I
b.
I
straight field in the center of a circular current
1. magnitude in center of solenoid, B = oI(N/L)
N/L = number of loops (N) per length (L)
2. direction: use rule from 2.a2 above, but reverse
thumb (B) and fingers (I)
into the page
out of the page
I
I
 
B
B
c.
north and south poles on a permanent magnet
1. magnetic field lines 
2.
no monopoles 
3.
north geographic pole is a "north seeking"
magnetic pole, which is actually a south
magnetic pole
B.
Induced emf, E (21-1 to 21-3, 21-7)
1. moving a wire loop relative to a magnetic field
generates (induces) an emf, E = B/t
a. adding loops (N) increases the effect: E = N(B/t)
b. magnetic flux,  B = A x B (T•m2)
magnetic field
Flux,  B, is like rain (B)
falling through a loop with
area
area, A
(maximum when AB)
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 in wire loop
a. I = E/R
b. Lenz's law: the magnetic field that induces
a current and the magnetic field produced
by the induced current are in the opposite
direction ( FB-induced opposes FB-inducing)
c. direction: use rule from A2.b2 above, but
flip your thumb 180o when B is
increasing, don't flip if B is decreasing,
induced current is in the direction that your
fingers wrap around your thumb
2. moving a conducting rod through a magnetic field
induces an emf, E = vLB
rod
rod at time t

  B (into the page)
c.
R  L 
v 



d = vt
Steps
Algebra
start with
E = B/t
substitute A x B for B
E = (A x B)/t
substitute Ld for A
E = (Ld x B)/t
substitute vt for d
E = (Lvt x B)/t
regroup
E = Lv(t/t) x B
simplify
E = vLB
a. induced current (in rod only), I = E/R = vLB/R
b. direction in the diagram: the magnetic field is into
the page (thumb), but increasing flux (flip your
thumb 180o) fingers wrap around your thumb in a
counterclockwise circle  induced current is
counterclockwise and is toward the top of the page
in the rod
3. 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)
Practice Problems
1.
A. Magnetic Properties
Determine the direction of FB for the following point charges.
Q
v
B
FB
a.
+
up
south
b.
–
south
c.
+
east
north
d.
–
east
up
e.
+
south
up
f.
+
down
south
east
up
g.
2.
down
north
h.
down
south
west
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.
3.
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.
4.
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.
5.
6.
7.
b.
kinetic energy.
c.
momentum.
Determine the following for a current carrying wire.
current
side
B
a.
east
above
b.
down
north
c.
south
south
d.
north
east
e.
west
south
f.
east
north
g.
north
west
h.
up
8.
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.
9.
Two long wires, r meters apart, carry currents of IA and IB
in opposite directions.
A
a.
b.
B
What is the magnitude and direction of magnetic field
generated by wire A at the position of wire B?
What is the magnitude and direction of the magnetic
force on a L-meter segment of wire B?
10. 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.
11. 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 B is (out of the page or into the page).
Determine 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.
west
i.
down
west
j.
west
north
k.
west
none
l.
south
up
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?
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.
12. 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?
13. Determine the magnitude and direction of the magnetic
field 1 m west of a long wire with a current of 100 A north.
14. Determine the magnitude and direction of the magnetic
field in the center of a thin 0.50-m-long solenoid that 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 m 2
and its electrical resistance is 10 .
a. Determine
B
E

I

b.
What is the direction of current?
19. A horizontal wire loop with area = 1 m2 and resistance = 5 ,
is in a downward 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 rod, with an internal resistance of 2 , moves along rails
that are 2 m apart through an upward 2-T magnetic field at
10 m/s east.
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
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
FB on the electron beam
in the rod
c. Calculate the current through the rod.
d.
Calculate the force needed to move the rod.
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.
b.
g.
Explain why the answers from parts e and f must be
the same.
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.
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 magnitude and direction of the induced current as
viewed from above.
Which shows the path that the electron follows?
(A) A
(B) B
(C) C
(D) D
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.
What is the direction of the magnetic field north of a wire
carrying a current east?
(A) west
(B) east
(C) down
(D) up
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.
9.
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.
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
5.
A counterclockwise current I in a circular loop of wire is
situated in a magnetic field directed out of the page.
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

What effect does the magnetic force have on the loop?
(A) it expands in size
(B) it contract in size
12. What is the induced current in the loop?
(A) 50 A
(B) 0.5 A
(C) 0.05 A (D) 5 A
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
13. What is the direction of the induced current?
(A) out of the paper
(B) into the paper
(C) clockwise
(D) counterclockwise
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
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
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.
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)
(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
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.
What is the induced emf in the wire loop of radius 2b?
(A) Zero
(B) E/2
(C) E
(D) 2E
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.
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.
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.
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
a.
In what direction must the magnetic field B point in
order to create the magnetic force?
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.
Determine the following given the values:
B = 5 T L = 10 m I = 200 A M = 0.5 kg D = 10 cm
d. speed of the bar as it reaches the end of the track.
Determine the following. Express answers in terms of the
quantities given above.
b. acceleration of the bar.
c.
e.
3.
speed of the bar as it leaves the end of the track.
the average power to the bar by the electric current.
Strontium ions (m = 1.45 x 10-25 kg) having a net charge of
3.2 x 10-19 C accelerate from rest through a potential
difference E after which the beam enters a region
containing a uniform 0.090-T magnetic field of constant
magnitude and perpendicular to the plane of the path of
the ions. The ions leave the magnetic field at a distance x
= 1.75 m from the entrance point.
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 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 x x x x
x x x x x x x
x x x x x x x
a. Calculate the magnetic flux B through the loop.
a.
In what direction must B point to produce the trajectory
of the ions shown?
The field strength now increases to 0.20 T in 0.50 s.
b. Calculate the emf E induced in the loop.
b.
The ions travel at constant speed around the semicircular path. Explain why the speed remains constant.
c.
Calculate the speed of the ions that exit at distance x.
d.
Calculate the accelerating voltage E needed for the
ions to attain the speed you calculated in part (c).

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.