Question 1

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

Accepted Answer

The answer of Four long straight wires carry equal currents...

Question 2

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

Accepted Answer

The answer of In Ampere's law, , the integration must...

Question 3

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

Accepted Answer

According to Ampere's law, the magnetic field inside a long cylindrical shell with a uniform current is given by B = μ₀i/2πr. Thus, inside the shell (R_i < r < R_o), the magnetic field is nonzero and depends on the radius r. However, outside the shell (r > R_o), the magnetic field is zero. Therefore, in order for the wire to experience no magnetic force, it must also have zero magnetic field. This can only happen if the wire is located on the axis of the cylinder, where the magnetic field is zero (r = 0). Furthermore, in order for the current in the wire to create a magnetic field that cancels the magnetic field inside the shell, the current in the wire must be in the opposite direction to that of the current in the shell. Thus, the correct answer is D.

Question 4

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

Accepted Answer

The force per unit length between two wires carrying currents is given by:

$$F = \frac{\mu_0 I_1 I_2}{2\pi d}$$

where $\mu_0$ is the permeability of free space, $I_1$ and $I_2$ are the currents in the wires, and $d$ is the distance between the wires.

In this case, we have $I_1 = 2$ A and $I_2 = -4$ A (since the currents are in opposite directions), and $d = 4$ cm = 0.04 m. Plugging in these values, we get:

$$F = \frac{(4\pi 	imes 10^{-7} 	ext{ T}\cdot	ext{m/A}) 	imes (2 	ext{ A}) 	imes (-4 	ext{ A})}{2\pi (0.04 	ext{ m})} = \frac{32\pi 	imes 10^{-7}	ext{ N}}{0.08	ext{ m}} = 4	imes 10^{-5} 	ext{ N/m}$$

Since the currents are in opposite directions, the two wires will experience a repulsive force, so the answer is (C).

Question 5

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

Accepted Answer

The path integral around the window frame is a closed loop around the current. Using Ampere's law, the magnetic field at all points on this loop is given by B = μ0I/2πr, where r is the distance from the current to the point on the loop. The smallest distance from the current to the loop is 1.5 m, and the largest distance is √(1.5^2 + 1^2) ≈ 1.8 m (the diagonal distance from one corner of the window to the opposite corner). Taking the average distance (1.65 m) and substituting in the values for μ0 and I, we get B = 2.0×10^-6 T. The length of the loop is 4.0 m, since there are two vertical sides of length 1.5 m and two horizontal sides of length 1.0 m. Therefore, the path integral of B · dl around the loop is 4.0 × (2.0×10^-6) = 8.0×10^-6 Wb = 3.8 × 10^(-7) V·s. Converting to units of Teslas·meters (the choices are all in this unit), we get 3.8 × 10^(-7) T·m = 3.8 × 10^(-10) T·km = 3.8 × 10^(-13) T·Mm = 3.8 × 10^(-16) T·Gm. The closest answer choice to this value is D, which is 3.8 × 10^(-16) T·m.

Question 6

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

Accepted Answer

The answer of Two parallel wires, 4 cm apart, carry...

Question 7

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

Accepted Answer

The answer of A long straight cylindrical shell has an...

Question 8

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

Accepted Answer

The answer of Two long straight wires enter a room...

Question 9

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

Accepted Answer

The answer of The magnetic field at any point in...

Question 10

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

Accepted Answer

The magnitude of the magnetic field at any radius r from the axis of the cylindrical shell is given by the formula B = μ0 * i * r / (2 * R^2), where R is the radius of the shell. Since the numerator i * r is maximized at the outer surface of the shell (r = R), and the denominator R^2 is the same for all radii, the magnitude of the magnetic field is greatest at the outer surface of the shell.

Question 11

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

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The answer of In Ampere's law, the direction of the...

Question 12

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

Accepted Answer

According to the Ampere's law, the net current passing through a closed loop is equal to the integral of the magnetic field over the surface bounded by the loop. Since the magnetic field is uniform over the circle, the integral of the magnetic field over the circle is also uniform and can be written as B times the area of the circle (B*pi*R^2). However, since the net current passing through the circle is not specified, we cannot use this information to calculate the net current. Therefore, the only possible answer is (A) 0, indicating that the net current passing through the circle is zero.

Question 13

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

Accepted Answer

The magnetic field inside a long ideal solenoid only depends on the cross-sectional area, the number of turns of wire, and the current. The spacing between the windings does not affect the magnetic field strength. Therefore, the correct choice is D.

Question 14

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

Accepted Answer

The answer of Two parallel long wires carry the same...

Question 15

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

Accepted Answer

The answer of Two parallel wires carrying equal currents of...

Question 16

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 -

Accepted Answer

The answer of In the figure, there are three wires...

Question 17

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

Accepted Answer

The answer of In Ampere's law, the symbol is:
A) an...

Question 18

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

Accepted Answer

When a constant current is sent through a helical coil, the coil tends to get shorter due to the magnetic field created by the current. This field exerts a force on different parts of the coil, pulling the turns of the coil closer together.

Question 19

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

Accepted Answer

The answer of A hollow cylindrical conductor (inner radius =...

Question 20

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

Accepted Answer

The answer of Magnetic field lines inside the solenoid shown...

Quiz 29: Magnetic Fields Due to Currents

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

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

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 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:

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 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:

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:

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

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

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

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:

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:

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:

In Ampere's law, the symbol is:

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

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?

Magnetic field lines inside the solenoid shown are: