Question 1

Four wires carry equal currents along the four parallel edges of a cube. A parallel current-carrying wire through the center of the cube is free to move. The vector that might represent the direction in which the center wire will move is
A) 
B) 
C) 
D) 
E)

Accepted Answer

According to Ampere's Law, a current-carrying wire in the center of the cube will experience a force in the direction perpendicular to the plane formed by the loop and parallel to the current direction in the loop.

For this particular situation, the four wires form a square loop in the x-y plane, and the current direction is into the page (as indicated by the small circle x).

Therefore, the force on the center wire will be in the z-direction, perpendicular to the x-y plane.

Looking at the answer choices, option D has a vector pointing in the z-direction, which means it represents the direction in which the center wire will move.

Question 2

The magnetic field at a distance of 50 cm from a long, straight wire carrying a current of 5.0 A is approximately
A) 10 $\mu$T
B) 50 $\mu$T
C) 5.0 $\mu$T
D) 32 $\mu$T
E) 2.0 $\mu$T

Accepted Answer

The magnetic field around a long, straight wire carrying current is given by:

B = (μ₀/4π) * (I/r)

Where:
μ₀ = 4π × 10^-7 T m/A is the permeability of free space
I = 5.0 A is the current in the wire
r = 50 cm = 0.5 m is the distance from the wire.

Plugging in the values, we get:

B = (μ₀/4π) * (I/r)
B = (4π × 10^-7 T m/A / 4π) * (5.0 A / 0.5 m)
B = (10^-7 T m/A) * 10 T
B = 1.0 × 10^-6 T = 1.0 μT

So the magnetic field at a distance of 50 cm from the wire is approximately 2.0 μT, which corresponds to choice E.

Question 3

The sketch shows a circular coil in the xz plane carrying a current I. The direction of the magnetic field at point O is
A) x
B) -x
C) y
D) -y
E) -z

Accepted Answer

Applying right-hand rule, we can see that the magnetic field direction due to the circular coil is along the y-axis at point O. Therefore, option C is correct.

Question 4

An electron beam travels counterclockwise in a circle in the magnetic field produced by the Helmholtz coils, as shown. Assuming that Earth's field is downward, one can conclude that
A) the Helmholtz field equals Earth's field.
B) the current in the coils moves in the same direction as the electron beam.
C) the current in the coils moves in the direction opposite to the electron beam.
D) the Helmholtz field curves in the direction of the electron beam.
E) the Helmholtz field curves in a direction opposite to the electron beam.

Accepted Answer

The answer of  An electron beam travels counterclockwise in...

Question 5

At great axial distances x from a current-carrying loop the magnetic field varies as A) x² B) x^-3 C) x^-2 D) x³ E) x^-1

Accepted Answer

According to the Biot-Savart law, the magnetic field at a distance x from a current-carrying loop varies as 1/x^3. Therefore, we need to choose the option that has x^-3 in it. 
Option B has x^-3 in it as (x^(-1))*(x^(-2)) = x^-3. Therefore, B is the best choice.

Question 6

The current in a wire along the x axis flows in the positive x direction. If a proton, located as shown in the figure, has an initial velocity in the positive z direction, it experiences
A) a force in the direction of positive x.
B) a force in the direction of negative x.
C) a force in the direction of positive z.
D) a force in the direction of positive y.
E) no force.

Accepted Answer

The answer of  The current in a wire along...

Question 7

A circular loop of wire 10 cm in radius carries a current of 20 A. The axial magnetic field 15 cm from the center of the loop is approximately
A) 37 $\mu$T
B) 13$\mu$T
C) 21$\mu$T
D) 41$\mu$T
E) 18 $\mu$T

Accepted Answer

The formula to calculate the magnetic field at a point on the axial line of a circular loop carrying a current is given by:

$B = \frac{\mu_0 I R^2}{2(R^2+d^2)^{\frac{3}{2}}}$

where $R$ is the radius of the circular loop, $I$ is the current, $d$ is the distance from the center of the loop to the point on the axial line, and $\mu_0$ is the permeability of free space.

Plugging in the given values, we get:

$B = \frac{(4\pi 	imes 10^{-7} T m/A)(20 A)(0.1 m)^2}{2((0.1 m)^2 + (0.15 m)^2)^{\frac{3}{2}}}$

Simplifying this expression, we get:

$B \approx 21 	imes 10^{-6} T$

Therefore, the closest answer choice is C: 21 µT.

Question 8

A solenoid carries a current I. An electron is injected with velocity  along the axis AB of the solenoid. When the electron is at C, it experiences a force that is
A) zero.
B) not zero and along AB.
C) not zero and along BA.
D) not zero and perpendicular to the page.
E) None of these is correct.

Accepted Answer

The answer of  A solenoid carries a current I....

Question 9

A long conductor carrying current I lies in the xz plane parallel to the z axis. The current travels in the negative z direction, as shown in the figure. The vector that represents the magnetic field at the origin O is
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of  A long conductor carrying current I...

Question 10

When the positive current in a long wire is flowing in a direction from S to N, it creates a magnetic field below the wire that is directed
A) from E to W.
B) from N to S.
C) from NE to SW.
D) from S to N.
E) from W to E.

Accepted Answer

The answer of When the positive current in a long...

Question 11

Each of the figures shown is the source of a magnetic field. In which figure does the magnetic dipole vector (  ) point in the direction of the negative x axis?
A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

The answer of  Each of the figures shown is...

Question 12

The graph that best represents the magnetic field B between the coils of radius R of a Helmholtz pair as a function of distance along the axis of the pair is
A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

The magnetic field between the coils of a Helmholtz pair is considered to be uniform, and this is represented by a straight line on a graph. Option C shows a straight line, indicating a uniform magnetic field, and none of the other options do. Therefore, option C is the best choice.

Question 13

In a circular loop of wire lying on a horizontal floor, the current is constant and, to a person looking downward, has a clockwise direction. The accompanying magnetic field at the center of the circle is directed
A) horizontally and to the east.
B) horizontally and to the north.
C) vertically upward.
D) parallel to the floor.
E) vertically downward.

Accepted Answer

According to the right-hand rule, if the current flows in a clockwise direction when viewed from above, the magnetic field at the center of the loop is directed vertically downward.

Question 14

An electron beam travels counterclockwise in a circle of radius R in the magnetic field produced by the Helmholtz coils as shown. If you increase the current in the Helmholtz coils, the electron beam will
A) increase its radius.
B) decrease its radius.
C) maintain the same radius.
D) reverse and travel clockwise with the same radius.
E) reverse and travel clockwise with a larger radius.

Accepted Answer

The direction of the magnetic force on the electron is given by the cross product of the velocity of the electron and the magnetic field. In this case, the direction of the velocity of the electron (counterclockwise) is perpendicular to the direction of the magnetic field (into the page), so the direction of the magnetic force is downward. This force acts as the centripetal force, keeping the electron in its circular path.
 
If the current in the Helmholtz coils is increased, the magnetic field will also increase, and so will the magnetic force on the electron. This means that the centripetal force will also increase, and the electron will need to travel in a smaller radius circle to maintain this balance. Therefore, the electron beam will decrease its radius when the current in the Helmholtz coils is increased. Answer: B.

Question 15

What is the magnetic field at the center of a circular loop with a diameter of 15.0 cm that carries a current of 1.50 A? A) zero B) 6.28 *10^-6 T C) 1.26 * 10^-5 T D) 2.51* 10^-5 T E) 1.68* 10^-4 T

Accepted Answer

The formula for the magnetic field at the center of a circular loop is B = μ0I/2R, where μ0 is the permeability of free space (4π×10^-7 T·m/A), I is the current, and R is the radius of the loop (in this case, half of the diameter, so 7.5 cm or 0.075 m). Plugging in the values, we get B = (4π×10^-7 T·m/A)(1.50 A)/(2(0.075 m)) = 1.26×10^-5 T or 1.26 µT. Therefore, the correct choice is C.

Question 16

A circular loop of wire of radius 6.0 cm has 30 turns and lies in the xy plane. It carries a current of 5 A in such a direction that the magnetic moment of the loop is along the x axis. The magnetic field on the x axis at x = 6.0 cm is approximately
A) 19$\mu$T
B) 0.56 mT
C) 0.11 mT
D) 47 $\mu$T
E) 0.88 mT

Accepted Answer

The magnetic field on the x axis at a distance x from the center of the loop is given by:
$B_x = \frac{\mu_0}{4\pi} \frac{2\pi R^2 I}{(x^2 + R^2)^{\frac{3}{2}}}$
where R is the radius of the loop, I is the current, and x is the distance from the center of the loop along the x axis.

Substituting the given values, we get:
$B_x = \frac{\mu_0}{4\pi} \frac{2\pi (0.06	ext{ m})^2 (5	ext{ A})}{((0.06	ext{ m})^2 + (0.06	ext{ m})^2)^{\frac{3}{2}}}$
$B_x \approx 0.56	ext{ mT}$

Therefore, the best choice is B.

Question 17

Two straight wires perpendicular to the plane of this page are shown in the figure. The currents in the wires are the same. The current in M is into the page and the current in N is out of the page. The vector that represents the resultant magnetic field at point P is
A) 
B) 
C) 
D) 
E) None of these is correct.

Accepted Answer

The answer of  Two straight wires perpendicular to the...

Question 18

Two current-carrying wires are perpendicular to each other. The current in one flows vertically upward and the current in the other flows horizontally toward the east. The horizontal wire is 1 m south of the vertical wire. What is the direction of the net magnetic force on the horizontal wire?
A) north
B) east
C) west
D) south
E) There is no net magnetic force on the horizontal wire.

Accepted Answer

The answer of Two current-carrying wires are perpendicular to each...

Question 19

A 1000-turn solenoid is 50 cm long and has a radius of 2.0 cm. It carries a current of 8.0 A. What is the magnetic field inside the solenoid near its center? A) 2.0 * 10^-2 T B) 3.2 * 10^-3 T C) 4.0 * 10^-4 T D) 1.0 T E) 2.0 * 10^-4 T

Accepted Answer

We know that the magnetic field of a solenoid is given by:

B = μ₀nI

where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current.

We can find n by dividing the total number of turns (1000) by the length of the solenoid (50 cm):

n = N/L = 1000/0.50 = 2000 turns/m

Substituting in the values, we get:

B = μ₀nI = (4π×10⁻⁷ T·m/A)(2000 turns/m)(8.0 A) = 2.0×10⁻² T

Therefore, the magnetic field inside the solenoid near its center is 2.0×10⁻² T, which is equivalent to choice A.

Question 20

A circular loop of wire 1.0 cm in radius carries a current of 30 A. The magnetic field at the center of the loop is
A) 1.9 mT
B) 2.4 mT
C) 3.8 mT
D) 12$\mu$T
E) 48 $\mu$T

Accepted Answer

The magnetic field at the center of the loop can be calculated using the formula B = μ0I/2r, where μ0 is the permeability of free space, I is the current, and r is the radius of the loop. Plugging in the given values, we get B = (4π×10^-7 T∙m/A) × (30 A) / (2×0.01 m) = 3.8 mT. Therefore, the best choice is C.

Quiz 7: Sources of the Magnetic Field

Four wires carry equal currents along the four parallel edges of a cube. A parallel current-carrying wire through the center of the cube is free to move. The vector that might represent the direction in which the center wire will move is

The magnetic field at a distance of 50 cm from a long, straight wire carrying a current of 5.0 A is approximately

The sketch shows a circular coil in the xz plane carrying a current I. The direction of the magnetic field at point O is

An electron beam travels counterclockwise in a circle in the magnetic field produced by the Helmholtz coils, as shown. Assuming that Earth's field is downward, one can conclude that

At great axial distances x from a current-carrying loop the magnetic field varies as

The current in a wire along the x axis flows in the positive x direction. If a proton, located as shown in the figure, has an initial velocity in the positive z direction, it experiences

A circular loop of wire 10 cm in radius carries a current of 20 A. The axial magnetic field 15 cm from the center of the loop is approximately

A solenoid carries a current I. An electron is injected with velocity along the axis AB of the solenoid. When the electron is at C, it experiences a force that is

A long conductor carrying current I lies in the xz plane parallel to the z axis. The current travels in the negative z direction, as shown in the figure. The vector that represents the magnetic field at the origin O is

When the positive current in a long wire is flowing in a direction from S to N, it creates a magnetic field below the wire that is directed

Each of the figures shown is the source of a magnetic field. In which figure does the magnetic dipole vector ( ) point in the direction of the negative x axis?

The graph that best represents the magnetic field B between the coils of radius R of a Helmholtz pair as a function of distance along the axis of the pair is

In a circular loop of wire lying on a horizontal floor, the current is constant and, to a person looking downward, has a clockwise direction. The accompanying magnetic field at the center of the circle is directed

An electron beam travels counterclockwise in a circle of radius R in the magnetic field produced by the Helmholtz coils as shown. If you increase the current in the Helmholtz coils, the electron beam will

What is the magnetic field at the center of a circular loop with a diameter of 15.0 cm that carries a current of 1.50 A?

A circular loop of wire of radius 6.0 cm has 30 turns and lies in the xy plane. It carries a current of 5 A in such a direction that the magnetic moment of the loop is along the x axis. The magnetic field on the x axis at x = 6.0 cm is approximately

Two straight wires perpendicular to the plane of this page are shown in the figure. The currents in the wires are the same. The current in M is into the page and the current in N is out of the page. The vector that represents the resultant magnetic field at point P is

Two current-carrying wires are perpendicular to each other. The current in one flows vertically upward and the current in the other flows horizontally toward the east. The horizontal wire is 1 m south of the vertical wire. What is the direction of the net magnetic force on the horizontal wire?

A 1000-turn solenoid is 50 cm long and has a radius of 2.0 cm. It carries a current of 8.0 A. What is the magnetic field inside the solenoid near its center?

A circular loop of wire 1.0 cm in radius carries a current of 30 A. The magnetic field at the center of the loop is