Question 1

Two parallel wires, 4 cm apart, carry currents of 2 A and 4 A respectively, in opposite directions. The force per unit length in N/m of one wire on the other is:

Accepted Answer

A)   1 * 10-3, repulsive
B)   1 *10-3, attractive
C)   4 * 10-5, repulsive
D)   4 * 10-5, attractive
E)   none of these C

Question 2

A long straight cylindrical shell has an inner radius Ri and an outer radius Ro. It carries a current i, uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the hollow region (r i). The magnetic field is zero everywhere outside the shell (r > Ro). We conclude that the wire:

Accepted Answer

A)   is on the cylinder axis and carries current i in the same direction as the current in the shell
B)   may be anywhere in the hollow region but must be carrying current i in the direction opposite to that of the current in the shell
C)   may be anywhere in the hollow region but must be carrying current i in the same direction as the current in the shell
D)   is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell
E)   does not carry any current D

Question 3

A toroid has a square cross section with the length of an edge equal to the radius of the inner surface. The ratio of the magnitude of the magnetic field at the inner surface to the magnitude of the field at the outer surface is:

Accepted Answer

A)   1/4
B)   1/2
C)   1
D)   2
E)   4 D

Question 4

A wire carrying a large current i from east to west is placed over an ordinary magnetic compass. The end of the compass needle marked "N" will point:

Accepted Answer

A)   north
B)   south
C)   east
D)   west
E)   the compass will act as an electric motor, hence the needle will keep rotating

Question 5

The magnitude of the magnetic field at point P, at the center of the semicircle shown, is given by:

Accepted Answer

A)   2 μ\muμ 0i/R2
B)    μ\muμ 0i/2  π\piπ R
C)    μ\muμ 0i/4  π\piπ R
D)    μ\muμ 0i/2R
E)    μ\muμ 0i/4R

Question 6

Two long straight wires enter a room through a window. One carries a current of 3.0 A into the room while the other carries a current of 5.0 A out. The magnitude in T.m of the path integral  around the window frame is:

Accepted Answer

A)   2.5* 10-6  T .m
B)   3.8 * 10-6 T . m
C)   6.3 * 10-6 T .m
D)   1.0 * 10-5 T .m
E)   none of these

Question 7

Helmholtz coils are commonly used in the laboratory because the magnetic field between them:

Accepted Answer

A)   can be varied more easily than the fields of other current arrangements
B)   is especially strong
C)   nearly cancels the Earth's magnetic field
D)   is parallel to the plane of the coils
E)   is nearly uniform

Question 8

The diagram shows three equally spaced wires that are perpendicular to the page. The currents are all equal, two being out of the page and one being into the page. Rank the wires according to the magnitudes of the magnetic forces on them, from least to greatest.

Accepted Answer

A)   1, 2, 3
B)   2, 1 and 3 tie
C)   2 and 3 tie, then 1
D)   1 and 3 tie, then 2
E)   3, 2, 1

Question 9

Two long straight wires are parallel and carry current in opposite directions. The currents are 8.0 A and 12 A and the wires are separated by 0.40 cm. The magnetic field in tesla at a point midway between the wires is:

Accepted Answer

A)   0
B)   4.0 * 10-4
C)   8.0 *10-4
D)   12* 10-4
E)   20 * 10-4

Question 10

If the radius of a pair of Helmholtz coils is R then the distance between the coils is:

Accepted Answer

A)   R/4
B)   R/2
C)   R
D)   2R
E)   4R

Question 11

The magnetic field a distance 2 cm from a long straight current-carrying wire is 2*10-5 T. The current in the wire is:

Accepted Answer

A)   0.16 A
B)   1.0 A
C)   2.0 A
D)   4.0 A
E)   25 A

Question 12

Which graph correctly gives the magnitude of the magnetic field outside an infinitely long straight current-carrying wire as a function of the distance r from the wire?

Accepted Answer

A)   I
B)   II
C)   III
D)   IV
E)   V

Question 13

Two long ideal solenoids (with radii 20 mm and 30 mm respectively) carry the have the same number of turnes of wire per unit length. The smaller solenoid is mounted inside the larger, along a common axis. It is observed that there is zero magnetic field within the inner solenoid is zero. The current in the inner solenoid must be:

Accepted Answer

A)   two-thirds the current in the outer solenoid
B)   one-third the current in the outer solenoid
C)   twice the current in the outer solenoid
D)   half the current in the outer solenoid
E)   the same as the current in the outer solenoid

Question 14

Two long parallel straight wires carry equal currents in opposite directions. At a point midway between the wires, the magnetic field they produce is:

Accepted Answer

A)   zero
B)   non-zero and along a line connecting the wires
C)   non-zero and parallel to the wires
D)   non-zero and perpendicular to the plane of the two wires
E)   none of the above

Question 15

In Ampere's law,  the symbol  is:

Accepted Answer

A)   an infinitesimal piece of the wire that carries current i
B)   in the direction of 
C)   perpendicular to 
D)   a vector whose magnitude is the length of the wire that carries current i
E)   none of the above

Question 16

The magnetic field at any point is given by  where  is the position vector of the point and A is a constant. The net current through a circle of radius R, in the xy plane and centered at the origin is given by:

Accepted Answer

A)     π\piπ AR2/ μ\muμ 0
B)   2  π\piπ AR/ μ\muμ 0
C)   4  π\piπ AR3/3 μ\muμ 0
D)   2  π\piπ AR2/ μ\muμ 0
E)     π\piπ AR2/2 μ\muμ 0

Question 17

In the figure, the current element  the point P, and the three vectors (1, 2, 3) are all in the plane of the page. The direction of  due to this current element, at the point P is:

Accepted Answer

A)   in the direction marked "1"
B)   in the direction marked "2"
C)   in the direction marked "3"
D)   out of the page
E)   into the page

Question 18

Solenoid 2 has twice the radius and six times the number of turns per unit length as solenoid 1. The ratio of the magnetic field in the interior of 2 to that in the interior of 1 is:

Accepted Answer

A)   2
B)   4
C)   6
D)   1
E)   1/3

Question 19

A toroid with a square cross section carries current i. The magnetic field has its largest magnitude:

Accepted Answer

A)   at the center of the hole
B)   just inside the toroid at its inner surface
C)   just inside the toroid at its outer surface
D)   at any point inside (the field is uniform) 
E)   at none of the above

Question 20

A "coulomb" is:

Accepted Answer

A)   one ampere per second
B)   the quantity of charge which will exert a force of 1 N on a similar charge at a distance of 1 m
C)   the amount of current in each of two long parallel wires separated by 1 m, which produces a force of 2 *10-7 N per meter
D)   the amount of charge which flows past a point in one second when the current is 1 A
E)   an abbreviation for a certain combination of kilogram, meter and second

Exam 29: Magnetic Fields Due to Currents