Deck 29: Magnetic Fields Due to Currents

Question 1

Two long straight current-carrying parallel wires cross the x axis and carry currents I and 3I in the same direction, as shown. At what value of x is the net magnetic field zero?

A) 0
B) 1
C) 3
D) 5
E) 7

Answer 1

3

Question 2

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

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

Answer 2

V

Question 3

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

Answer 3

20 * 10^-4 T

Question 4

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

A) 2 $\mu$ ₀i/R²
B) $\mu$ ₀i/2 $\pi$ R
C) $\mu$ ₀i/4 $\pi$ R
D) $\mu$ ₀i/2R
E) $\mu$ ₀i/4R

Question 5

Electrons are going around a circle in a counterclockwise direction as shown. At the center of the circle they produce a magnetic field that is:

A) into the page
B) out of the page
C) to the left
D) to the right
E) zero

Question 6

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) 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 7

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:

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

Question 8

Suitable units for $\mu$ ₀ are:

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

Question 9

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

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 10

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:

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 11

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:

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

Question 12

Lines of the magnetic field produced by a long straight wire carrying a current are:

A) in the direction of the current
B) opposite to the direction of the current
C) leave the wire radially
D) circles concentric with the wire
E) lines similar to those produced by a bar magnet

Question 13

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?

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 14

In an overhead straight wire, the current is north. The magnetic field due to this current, at our point of observation, is:

A) east
B) up
C) north
D) down
E) west

Question 15

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:

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 16

The magnetic field outside a long straight current-carrying wire depends on the distance R from the wire axis according to:

A) R
B) 1/R
C) 1/R²
D) 1/R³
E) 1/R^3/2

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.

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

Question 18

A coulomb is:

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 19

Two long straight wires pierce the plane of the paper at vertices of an equilateral triangle as shown below. They each carry 2.0 A, out of the paper. The magnetic field at the third vertex (P) has magnitude:

A) 5.0 * 10^-6 T
B) 8.7 *10^-6 T
C) 1.0 * 10^-5 T
D) 1.7* 10^-5 T
E) 2.0 * 10^-5 T

Question 20

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.

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

Question 21

Four long straight wires carry equal currents into the page as shown. The magnetic force exerted on wire F is:

A) north
B) east
C) south
D) west
E) zero

Question 22

In Ampere's law, , the integration must be over any:

A) surface
B) closed surface
C) path
D) closed path
E) closed path that surrounds all the current producing

Question 23

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

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 24

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:

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 25

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:

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 26

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:

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 27

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

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 28

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 of the path integral around the window frame is:

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 29

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) $\pi$ 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

Question 30

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

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

Question 31

In Ampere's law, the direction of the integration around the path:

A) must be clockwise
B) must be counterclockwise
C) must be such as to follow the magnetic field lines
D) must be along the wire in the direction of the current
E) none of the above

Question 32

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

Question 33

The magnetic field inside a long ideal solenoid is independent of:

A) the current
B) the number of turns of wire
C) the spacing of the windings
D) the cross-sectional area
E) the direction of the current

Question 34

Two parallel long wires carry the same current and repel each other with a force F per unit length. If both these currents are doubled and the wire separation tripled, the force per unit length becomes:

A) 2F/9
B) 4F/9
C) 2F/3
D) 4F/3
E) 6F

Question 35

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:

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

Question 36

In the figure, there are three wires carrying currents in the indicated directions, and an Amperian loop. The sign of the contribution of the current in each wire to the path integral in Ampere's Law is:

A) i₁ +, i₂ -, i₃ 0
B) i₁ -, i₂ +, i₃ 0
C) i₁ +, i₂ +, i₃ -
D) i₁ -, i₂ -, i₃ +
E) i₁ +, i₂ -, i₃ -

Question 37

In Ampere's law, the symbol is:

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 38

A constant current is sent through a helical coil made of flexible wire. The coil:

A) tends to get shorter
B) tends to get longer
C) tends to rotate about its axis
D) produces zero magnetic field at its center
E) none of the above

Question 39

A hollow cylindrical conductor (inner radius = a, outer radius = b) carries a current i uniformly spread over its cross section. Which graph below correctly gives B as a function of the distance r from the center of the cylinder?

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

Question 40

Magnetic field lines inside the solenoid shown are:

A) clockwise circles as one looks down the axis from the top of the page
B) counterclockwise circles as one looks down the axis from the top of the page
C) toward the top of the page
D) toward the bottom of the page
E) in no direction since B = 0

Question 41

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:

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

Question 42

Two long ideal solenoids (with radii 20 mm and 30 mm respectively) have the same number of turns 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. The current in the inner solenoid must be:

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 43

The diagram shows three arrangements of circular loops, centered on vertical axes and carrying identical currents in the directions indicated. Rank the arrangements according to the magnitudes of the magnetic fields at the midpoints between the loops on the central axes, from least to greatest.

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

Question 44

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?

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 45

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

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 46

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

Question 47

If R is the distance from a magnetic dipole, then the magnetic field it produces is proportional to:

A) R²
B) R
C) 1/R
D) 1/R²
E) 1/R³

Question 48

A 45-m long wire is coiled so that it makes a coil containing 100 circular loops, one on top of the other. If the wire carries a current of 13 A, what is the magnetic dipole moment of the coil?

A) 21 A·m²
B) 6.7 A·m²
C) 3.3 A·m²
D) 2.6 A·m²
E) 1.2 A·m²

Question 49

A solenoid is 3.0 cm long and has a radius of 0.50 cm. It is wrapped with 500 turns of wire carrying a current of 2.0 A. The magnetic field at the center of the solenoid is:

A) 9.9 *10^-8 T
B) 1.3 *10^-3 T
C) 4.2 * 10^-2 T
D) 16 T
E) 20 T