Question 1

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 
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 B

Question 2

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

Accepted Answer

A) " $\pi$ AR2/ $\mu$ 0" 
B) "2 $\pi$ AR/ $\mu$ 0" 
C) "4 $\pi$ AR3/3 $\mu$ 0" 
D) "2 $\pi$ AR2/ $\mu$ 0" 
E) " $\pi$ AR2/2 $\mu$ 0" 
A) " $\pi$ AR2/ $\mu$ 0" 
B) "2 $\pi$ AR/ $\mu$ 0" 
C) "4 $\pi$ AR3/3 $\mu$ 0" 
D) "2 $\pi$ AR2/ $\mu$ 0" 
E) " $\pi$ AR2/2 $\mu$ 0" D

Question 3

A long straight cylindrical shell carries current i uniformly distributed over its cross section.The magnitude of the magnetic field is greatest:

Accepted Answer

A) at the inner surface of the shell 
B) at the outer surface of the shell 
C) inside the shell near the middle 
D) in hollow region near the inner surface 
E) near the center of the hollow region 
A) at the inner surface of the shell 
B) at the outer surface of the shell 
C) inside the shell near the middle 
D) in hollow region near the inner surface 
E) near the center of the hollow region B

Question 4

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

Question 5

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 
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

Question 6

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 at a point midway between the wires is:

Accepted Answer

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

Question 7

A semi-infinite wire runs along the positive y axis, beginning at the origin (x = y = 0)and extending infinitely far in the +y direction.If the current in the wire is 12 A, what magnetic field does it create on the x axis at the point x = 3.5 cm?

Accepted Answer

A) 0 T 
B) 3.4 x 10-5 T 
C) 6.9 x 10-5 T 
D) 1.4 x 10-4 T 
E) 4.3 x 10-4 T 
A) 0 T 
B) 3.4 x 10-5 T 
C) 6.9 x 10-5 T 
D) 1.4 x 10-4 T 
E) 4.3 x 10-4 T

Question 8

An ordinary magnetic compass is placed flat on the ground.A wire carrying a large current i from east to west is placed directly above the 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 
A) north 
B) south 
C) east 
D) west 
E) the compass will act as an electric motor, hence the needle will keep rotating

Question 9

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

Accepted Answer

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

Question 10

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 
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 11

If the magnetic field   is uniform over the area bounded by a circle with a radius R, the net current through the circle is:

Accepted Answer

A) "0" 
B) "2 $\pi$ RB $\mu$ 0" 
C) " $\pi$ R2B/ $\mu$ 0" 
D) "RB/2 $\mu$ 0" 
E) "2RB/ $\mu$ 0" 
A) "0" 
B) "2 $\pi$ RB $\mu$ 0" 
C) " $\pi$ R2B/ $\mu$ 0" 
D) "RB/2 $\mu$ 0" 
E) "2RB/ $\mu$ 0"

Question 12

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 
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

Question 13

A long straight wire carrying a 3.0 A current enters a room through a window 1.5 m high and 1.0 m wide.The path integral   around the window frame has the value:

Accepted Answer

A) 0.20 T.m 
B) 2.5* 10-7 T.m 
C) 3.0 *10-7 T.m 
D) 3.8 * 10-6 T.m 
E) none of these 
A) 0.20 T.m 
B) 2.5* 10-7 T.m 
C) 3.0 *10-7 T.m 
D) 3.8 * 10-6 T.m 
E) none of these

Question 14

Suitable units for  $\mu$ 0 are:

Accepted Answer

A) tesla 
B) newton/ampere2 
C) weber/meter 
D) kilogram.ampere/meter 
E) tesla.meter/ampere 
A) tesla 
B) newton/ampere2 
C) weber/meter 
D) kilogram.ampere/meter 
E) tesla.meter/ampere

Question 15

In the figure, if the current element has a length of 1.0 mm, carries a current of 2.5 A, and is a distance of 4.8 cm from the point P, what is the magnitude of the magnetic field at point P?

Accepted Answer

A) 0 T 
B) 2.6 x 10-9 T 
C) 5.4 x 10-8 T 
D) 9.4 x 10-8 T 
E) 1.1 x 10-7 T 
A) 0 T 
B) 2.6 x 10-9 T 
C) 5.4 x 10-8 T 
D) 9.4 x 10-8 T 
E) 1.1 x 10-7 T

Question 16

A square loop of current-carrying wire with edge length a is in the xy plane, the origin being at its center.Along which of the following lines can a charge move without experiencing a magnetic force?

Accepted Answer

A) x = 0, y = a/2 
B) x = a/2, y = a/2 
C) x = a/2, y = 0 
D) x = 0, y = 0 
E) x = 0, z = 0 
A) x = 0, y = a/2 
B) x = a/2, y = a/2 
C) x = a/2, y = 0 
D) x = 0, y = 0 
E) x = 0, z = 0

Question 17

The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r)and radial lengths.The circuits carry the same current.Rank them according to the magnitudes of the magnetic fields they produce at C, least to greatest.

Accepted Answer

A) 1, 2, 3 
B) 3, 2, 1 
C) 1, 3, 2 
D) 2, 3, 1 
E) 2, 1, 3 
A) 1, 2, 3 
B) 3, 2, 1 
C) 1, 3, 2 
D) 2, 3, 1 
E) 2, 1, 3

Question 18

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

Accepted Answer

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

Question 19

Two parallel wires carrying equal currents of 10 A attract each other with a force of 1 mN.If both currents are doubled, the force of attraction will be:

Accepted Answer

A) 0.25 mN 
B) 0.5 mN 
C) 1 mN 
D) 2 mN 
E) 4 mN 
A) 0.25 mN 
B) 0.5 mN 
C) 1 mN 
D) 2 mN 
E) 4 mN

Question 20

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

Accepted Answer

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

Exam 29: Magnetic Fields Due to Currents

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

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

A long straight cylindrical shell carries current i uniformly distributed over its cross section.The magnitude of the magnetic field is greatest:

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:

A coulomb is:

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 at a point midway between the wires is:

A semi-infinite wire runs along the positive y axis, beginning at the origin (x = y = 0)and extending infinitely far in the +y direction.If the current in the wire is 12 A, what magnetic field does it create on the x axis at the point x = 3.5 cm?

An ordinary magnetic compass is placed flat on the ground.A wire carrying a large current i from east to west is placed directly above the compass.The end of the compass needle marked "N" will point:

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

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

If the magnetic field is uniform over the area bounded by a circle with a radius R, the net current through the circle is:

A long straight wire carrying a 3.0 A current enters a room through a window 1.5 m high and 1.0 m wide.The path integral around the window frame has the value:

Suitable units for μ\muμ 0 are:

In the figure, if the current element has a length of 1.0 mm, carries a current of 2.5 A, and is a distance of 4.8 cm from the point P, what is the magnitude of the magnetic field at point P?

A square loop of current-carrying wire with edge length a is in the xy plane, the origin being at its center.Along which of the following lines can a charge move without experiencing a magnetic force?

The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r)and radial lengths.The circuits carry the same current.Rank them according to the magnitudes of the magnetic fields they produce at C, least to greatest.

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

Two parallel wires carrying equal currents of 10 A attract each other with a force of 1 mN.If both currents are doubled, the force of attraction will be:

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

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Suitable units for $\mu$ ₀ are: