**USEFUL CONSTANTS: u _{0} = 4pi
x 10^{-7}
T·m/A q
(electron) = -1.6 x 10^{-19} C**

5] Two infinitely long, current carrying wires

are shown in the figure to the right.

(A) What is the magnitude and direction of the net magnetic
field

at point, X, midway between
the wires?

ANSWER: 5.0 x 10^{-5} T into the
paper

(B) What would be the force per unit length on a third wire,
placed

at position X and running parallel
to the other two if it carries a

current of 10 A. (** no need to
give force direction here)

ANSWER: 5.0 x 10^{-4} N/m

6] A solenoid with 2000 turns per meter carries a current of 15.0 A
. A single loop of wire of cross-sectional area, A = 3.14 x 10^{-4}
m^{2}, is placed against the left end of the solenoid. The
current
in the solenoid is turned

off such that the magnetic field in the solenoid goes to zero in 3.00
x 10^{-3} sec.

What would be the average induced emf across a small break in the wire loop during the time the field goes to zero?

ANSWER: emf = 0.0040 V

1] A magnetic field of 2.50
x 10^{-4}
T is directed into the paper. A proton ( mass = 1.67 x 10^{-27}
kg ) moving upward in the plane of the paper

experiences
a force of 2.0 x 10^{-16} N. Determine the **radius
of the circular path** the proton will follow and state which **direction**

** (CW or
CCW) the proton moves**.

ANSWER: 209
meters
CCW

2] A conducting bar of
length
12 cm slides along two conducting rails in the presence of a 0.10 T
magnetic
field directed out of the page.

What
velocity
must the bar have such that the emf induced across it is, e=
12V ?

ANSWER: 1000 m/s

3] The magnetic field 10 cm
from
a long straight wire is found to be 1.0 x 10^{-5} T. If the
wire
is now coiled into a 500 loop solenoid with a

magnetic
field
of 1.5 x 10^{-3} T, how long is the wire?

ANSWER: 2.1 meter

4] A magnetic field of 2.5 x
10^{-4}
T is directed into the paper (the -z direction). A wire that lies in
the
plane of the paper (the x,y plane) makes

an angle of
30^{o} with the x axis and carries a current of 3.0
A.
What is the magnitude and direction of the force per unit length on the
wire

due to the
magnetic field?

Multiple Choice
Examples

1. The direction of the force on a
current-carrying wire in a magnetic field is described by which of the
following?

a) perpendicular to the current

b) perpendicular to the magnetic
field

c) parallel to the current

d) both a) and b) are valid

e) neither a) nor b) is valid

2. Two long parallel wires carry equal
currents. The magnitude of the force between the wires is
F. The current in each wire is then doubled.

What is the magnitude of the new force between
the two wires?

a) 4F

b) 2F

c) F

d) F/2

e) F/4

3. According to Lenz's law, the
direction of an induced current in a conductor will be that which tends
to produce which of the following effects?

a) enhance the efffect which
produces it

b) produce a greater heating
effect

c) produce the greatest voltage

d) oppose the effect which
produces it

e) none of the above

4. The magnetic field of the Earth can
be represented by magnetic field lines most similar to those produced
by

a) a horseshoe magnet

b) a magnetic monopole

c) an infinitely long solenoid

d) a magnetic dipole

e) a magnetic quadrupole

Answers:

1. d

2. a

3. d

4. d