For the wire carrying a flow of
electrons in the direction
shown, is the

magnetic field B at point P
P
(a) to the right
(b) to the left
(c) up
(d) into the screen
(e) out of the screen
In the figure below, which is the
direction of the magnetic field at
point…
1) …P?
(a)
2) …Q?
(b)
(c)
3)…R?
(d)
(e)
In the figure above, where is the magnetic
field the weakest?
(a) point P
(b) point Q
(c) point R

ds2
Biot - Savart law


ds  r
dB  k m I
r2

ds1

r2
I
P

r1
The magnetic field at P due to the current I in
1. ds1
2. ds2
3. ds3
4. ds4
Is directed
(a) into the screen
(b) out of the screen
(c) up
(d) down
(e) zero

r3

ds3

ds4

r4

ds
I


r
I
P


ds  r
Biot - Savart law: dB  k m I
r2
The magnitude of the magnetic field contribution from the current

element ds above is
ds  1 sin 90o
a ) dB  km I
r2
ds  r  cos 90o
b) dB  km I
r2
ds  1 sin 
c) dB  km I
r2
d ) none of the above

ds
The total magnetic field at P
I
I
from the current in the wire
P
shown on the right is:
Biot - Savart law: B  dB  k I ds  rˆ
m
2
Ir
BP  k m 2
r
Ir
BP  k m 2
r
I 2 r
BP  k m
r2
I ds sin 90o
BP  k m
r2
none of the above
2
a)
b)
c)
d)
e)


r
Ids sin90o
dB  km
r2


ds  r
dB  k m I
The Biot-Savart law for the contribution
r2
to the magnetic field from a current

ds  r

so dB  dB  k m I
sin 
element I ds is given on the right.
2
r
P
Use the figure to answer the
following questions about the
Biot-Savart Law
r1
n
1
3
r
I) Is the ‘r’ given by (a) r1 (b) r2 (c) r3 ?
II) Is the 2 given by (a) 21 (b) 22 (c) 23 ?
III) Is the direction of at P
(a) up
(b) down
(c)into page
(d)out of page
2
3
r2
I
Magnetic field from a section of a straight wire

r = vector of length 1 in the r direction

r
r
I

ds

ds  r
Biot Savart law: dB  km I 2
r

The magnitude of the magnetic field at P due to the current I in ds is
ds  1
(a ) dB  km I
r2
I ds cos 
(c) dB  km
r2
(e) None of the above
I ds sin 
(b) dB  km
r2
I ds  r  sin 
(d ) dB  km
r2
Magnetic field from a section of a straight wire
km I
BP 
cos1  cos2 
a
Given the equation and figure
on the right, what is the field
at P due to an infinitely long
wire carrying current I?
P
a ) BP 

b)






c)
d)
e)
km I
cos 40o  cos150o
a
km I
BP 
cos 0o  cos 360o
a
km I
BP 
cos 0o  cos180o
a
k I
BP  m cos180o  cos 0o
a
none of the above

1
2
a
I
BP 
1
km I
cos1  cos2 
a
P
a
I
I
2
a
P
a
I
Equilateral
triangle
a
I
Figure 1
Figure 2
The magnetic field at a distance “a” from a straight wire carrying
current I is given in Figure 1. Therefore, the field at point P in
Figure 2 is:
km I
(a) BP  3
cos 30o  cos150o
a
(b) BP  0

km I
o
o
(c) BP  3
cos
60

cos
0


a
km I
(d) BP  2
a

For the two long wires on the right, the vector

magnetic field at P is best represented by Bp
where...

BP
P
(a)
P
(b)

BP
(c)

BP
P
P
(d)
(e) none of the above

BP
I
P
I
Two wires carry equal currents I1 into the screen, each producing
a magnetic field B1 at point P
I1
y

P

x
I1
The total field at P is given by
(a)
B1
(b)
2B1
(c)
2B1cos xˆ
-2B1sin yˆ
(d)
-2B1cos yˆ
(e)
Magnetic field on the axis of a circular turn of wire

dsu

dsu
I
P

dsd
Perspective
view
dB3
x
 o ds  r
dB 
I 2
4
r
dB1
dB2
P
dB4

dsd
dB6
dB5
Top view

1. Which best represents the field at P from i) I dsu and ii) I dsd ?
(a)
dB1 (b) dB2 (c) dB3 (d) dB4
(e) dB
5
2. Which best represents the total field at P?
(a)
dB1 (b) dB2 (c) dB3 (d) dB4
(e) dB
6
x
Magnetic field on the axis of a solenoid
Which of the following is the equation for the magnetic field on
the axis of a solenoid?
a) B 
o IR
2
2( x  R )
o NI
b) B 
cos1  cos2 
2
o I
c) B 
cos1  cos2 
4a
d ) none of the above
2
2
Magnetic field on the axis of a solenoid
N
turns per meter
L
I
1. Is the field at P1 directed
(a) to the right
I
L
(b) to the left
2
(c) neither
P2
P1
1
BP 
2. Near the centre of a long solenoid, is BP1
 NI
NI
NI
(a) o
(b) o
(c) 2o
(d) none of these
2 L
L
L
3. Near one end of a long solenoid, is BP2
o NI
NI
NI
(a)
(b) o
(c) 2o
(d) none of these
2 L
L
L
o NI
2 L
cos1  cos2 
Three equations from the formula sheet are given below for the
magnetic field caused by a current I.
 o IR 2
km I
(a) BP 
(b) B 
(cos1  cos 2 )
2
2 3/ 2
p
2( R  x )
a
oI

(cos1  cos 2 )
4 a
 o NI
(c) BP 
[cos1  cos 2 ]
2 L
Which of these is the correct one to use for the
magnetic field…
1. …at a given distance from a straight wire
2. …on the axis of a circular turn
3. …on the axis of a solenoid (coil)
L
Current I flows in
the coil on the right
I
N turns
N
m
L

I
w
 
Ampere's law:  B  ds  o I enclosed
Assuming B= 0 just outside the coil, use
Ampere's law and the dotted path provided to
determine the field B on the axis of the coil.
(a) B 
o I
L
Im
(c) B  o
L
(b) B  o I m
(d) None of the above
w

 
Ampere's law:  B  ds  o I enclosed
Current I flows in the
coil on the right
L
N turns
I
N
m
L
I
Redraw the coil on your page, and
(a) Sketch the shape and direction of the magnetic field near one of the wire turns at
the bottom.
(b) Sketch the shape and direction of the magnetic field
near a turn adjacent to the one in (a).
(c) Do the fields in (a) and (b) add or subtract along the
axis of the coil?
(d) Do these fields in (a) and (b) add or subtract in the
region between two adjacent wires?
(e) Draw a magnetic field line just inside the line of wires
on the bottom of the coil.
 
Ampere's law:  B  ds  o I enclosed
Current I flows in the
coil on the right
L
I
N turns
N
m
L
I
Redraw the coil on your page, and
(1) Sketch the shape and direction of the magnetic field near one of the wire turns
at the top.
(2) Does the field in (a) reinforce or cancel the
corresponding field from a turn at the bottom of the coil?
Inside the coil: (a) reinforce
(b) cancel
Outside the coil: (a) reinforce
(b) cancel
(3) From our discussion to date, sketch a few field lines
around and inside the whole coil. Remember that the field
lines are closest together where B is strongest.
 
Ampere's law:  B  ds  o I enclosed
The magnetic field lines around a
solenoid look roughly as sketched on
the right
B
To calculate B on the axis of the solenoid,
select a closed path, containing some
current and consisting of several
segments, such that for each segment
either (i) B ~ 0, or (ii) B z path, or (iii)
B ~ constant andB
path
I (into screen)
I
I
I
.
Either (b) or (c)
I
(a)
(b)
(c)
(d)
I (out of screen)
 
Ampere's law:  B  ds  o I enclosed
A large wire of radius R carries a current I0 into the
screen as sketched on the right. The current is
uniformly distributed over the wire. Ampère's law is
used to determine the magnetic field strength B at a
distance r from the centre of the wire.

ds
P
1. For the dashed path, how much current is Ienclosed?
r
R
r 2
I0
I 0 (c)
(a) I0
(b)
(d)
2 I0
R
r 
R
2. At point P, is B  ds: (a) B ds (b) zero (c) can't tell?
3. Which is the correct result for B(r) from
Ampère's law?
(a) B(r )r 2 
0 Ienclosed (d) B(r ) ds  0 I enclosed
(b)B(r ) 4r 2  0 Ienclosed (e) B(r ) 2r  0 I enclosed
(c) B(r ) r  0 I enclosed
r
R
-
  
v
  

B
into screen
  
F  qv  B
What is the direction of the force on the particle?
(a) into screen
(d) down
(b) out of screen
(e) to right
Does the particle rotate
(a) clockwise? (b) counterclockwise?
(c) up
 in a circle in a
For a charged particle
moving
with
velocity
v

magnetic field B , which of the following is most correct?

 
(a) F  qv  B
(b)
 mv 2
(d) F 
r
(e) a, b and c
m v2
F
r
(c)
F  qvBsin 
Which of the following is the correct angular velocity
of a particle of charge q moving perpendicular to a
magnetic field B?
(a)  
m
qB
(b)  
B
m
(d)  
qB
m
(e)  
qvB
m
(c)   qvBm
What is the direction of the magnetic force on the negative particle
q below, caused by the magnetic field from the wire?
q
I

 
F  qv  B
a) Up
b) Down
c) Into screen
d) Out of screen

v
I
(From pre-class quiz)
Distribution of charge in a current sheet, in a magnetic field
A steady conventional current, I, is flowing northward in a horizontal
conducting sheet, and a magnetic field is oriented downwards through
the sheet. Which of the following statements is true?
a. The East edge of the sheet will carry no net charge.
b. The East edge of the sheet is positively charged.
c. The East edge of the sheet is negatively charged.
d. Both the East and the West edges of the sheet are
positively charged.

B
I
1. Which side of the metal ribbon
shown on the right is positive?
(a) a
(b) b
(c) c
(d) d
z
b
a
c
I
d
2. What direction is the electric field in the ribbon, caused by the
magnetic field?
(a) xˆ
(d)  yˆ
(b)  xˆ
(e)  zˆ
(c) yˆ
y
x

B into the page
wire
I
I
 

Fon wire  I   B
The charge carriers in the wire are electrons. What is the direction
of the magnetic force on the wire?
(a) out of the page
(b) up
(c) down
(d) to right
(e) to left
Two long wires carry current
into the screen.
 

F  I  B
A
B
1. What is the direction of the magnetic field at B caused by A?
(a) to the right
(b) to the left
(c) up
(d) down
2. Is the direction of the force on B
(a) up
(b) down
(c) into screen
(d) out of screen (e) to the left
3. Do the two wires
(a) attract each other
(c) neither
(b) repel each other
#1
#2
Two long parallel wires carry currents,
I1
I2 > I1
I1 into the screen and I2 > I1 out of the
screen.
1. What is the direction of the force on i) wire #1? ii) wire #2?
(a)
(b)
(c)
(d)
(e)
No force
2. Compared to the force on wire #1, the force
on #2 is
(a) greater
(b) smaller
(c) the same?
3. What entirely independent method could you
use to determine the direction in question 1. ii)
given the answer in 1. i)?
A rectangular loop is placed in a uniform
magnetic field with the plane of the loop
perpendicular to the direction of the field.
If a current is made to flow through the loop
in the sense shown by the arrows, the field
exerts on the loop:

B
I
1. a net force.
2. a net torque.
3. a net force and a net torque.
4. neither a net force nor a net torque.
PI
A rectangular loop is placed in a uniform
magnetic field with the plane of the loop
parallel to the direction of the field.
If a current is made to flow through the loop
in the sense shown by the arrows, the field
exerts on the loop:

B
I
1. a net force.
2. a net torque.
3. a net force and a net torque.
4. neither a net force nor a net torque.
PI

What is A for this current loop?
 
  IA  B

2
y
z
1
a)
c)
b)  Izˆ
Izˆ
1 2
zˆ
d) 
1 2
zˆ
x

A rectangular loop of wire carries a current I in a magnetic field B
I
F  I B
l1

B
S
N

l2
Top view
l2


B
Which of the following gives the force on one
side of the loop?
(a) F  Il1B
(b) F  Il2 B
(c) F  Il1B cos 
(d) F  Il1B sin 
(e) F  Il2 B sin 
z
y
x

A rectangular loop of wire carries a current I in a magnetic field B

B
S
N

z
Top view
N

y
x
S
In which direction does
 the coil rotate (direction
of angular velocity  )?
(a)  xˆ
(d)  zˆ
(b)  yˆ
(e)  zˆ
(c)  yˆ

A rectangular loop of wire carries a current I in a magnetic field B
I
  IA  B
l1

B
S
N

l2
Top view
l2
z


B
Which of the following gives the torque on the
loop?
(a)   Il1B cos 
(b)  Il1l2 B cos 
(c)   Il1l2 B sin 
(d)   2 Il1l2 B sin 
(e)   Il1l2 B
y
x
P
The
Galvanometer
If the current flows through the galvanometer coil
in the direction of the bold arrows, does the
pointer P deflect ?
(a) clockwise
(b) counterclockwise
(c) not enough information to tell