EXAM 3  Practice Problems

USEFUL CONSTANTS: u0 = 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 m2, 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 30o 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?

    ANSWER:  7.5 x 10-4 N/m    directed in the -y direction (toward bottom of page)


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


1.  d
2.  a
3.  d
4.  d