Question 1

Two long parallel wires carry currents of 5.0 A and 8.0 A in the opposite direction. The wires are separated by 0.30 m. Find the magnetic force per unit length between the two wires. A)2.7 × 10^-⁵ N/m repulsive B)7.2 × 10^-⁵ N/m repulsive C)3.4 × 10^-⁵ N/m attractive D)2.7 × 10^-⁵ N/m attractive E)7.2 × 10^-⁵ N/m attractive

Accepted Answer

The magnetic force between two parallel wires carrying currents in opposite directions is repulsive. The magnitude of the force per unit length is given by:$$F = \frac{\mu_0 I_1 I_2}{2\pi d}$$where:* $\mu_0$ is the permeability of free space ($4\pi 	imes 10^{-7} 	ext{ T}\cdot	ext{m/A}$)* $I_1$ and $I_2$ are the currents in the wires (5.0 A and 8.0 A)* $d$ is the distance between the wires (0.30 m)Plugging in the values, we get:$$F = \frac{(4\pi 	imes 10^{-7} 	ext{ T}\cdot	ext{m/A})(5.0 	ext{ A})(8.0 	ext{ A})}{2\pi (0.30 	ext{ m})}$$$$F = 2.7 	imes 10^{-5} 	ext{ N/m}$$Therefore, the magnetic force per unit length between the two wires is $2.7 	imes 10^{-5} 	ext{ N/m}$ repulsive.

Question 2

A straight wire carries a 12-A current eastward and a second straight wire carries a 14-A current westward. The wires are separated by a distance of 42 cm. The force per unit length on the wire carrying 12 A is A)8.0 × 10^-5 N/m. B)5.1 × 10^-7 N/m. C)5.1 × 10^-4 N/m. D)5.1 × 10^-6 N/m. E)8.0 × 10^-7 N/m.

Accepted Answer

The force per unit length on the wire carrying 12 A is given by:$$F = \frac{\mu_0}{4\pi} \frac{2I_1I_2}{d}$$where:$$\mu_0$$ is the permeability of free space ($$4\pi 	imes 10^{-7} 	ext{ T}\cdot	ext{m/A}$$)$$I_1$$ is the current in the first wire (12 A)$$I_2$$ is the current in the second wire (14 A)$$d$$ is the distance between the wires (42 cm = 0.42 m)Plugging in the values, we get:$$F = \frac{4\pi 	imes 10^{-7} 	ext{ T}\cdot	ext{m/A}}{4\pi} \frac{2(12 	ext{ A})(14 	ext{ A})}{0.42 	ext{ m}} = 8.0 	imes 10^{-5} 	ext{ N/m}$$Therefore, the correct answer is A.

Question 3

A solenoid of 200 turns carrying a current of 2 A has a length of 25 cm. What is the magnitude of the magnetic field at the center of the solenoid?
A)2 mT
B)3 mT
C)4 mT
D)5 mT
E)6 mT

Accepted Answer

The answer of A solenoid of 200 turns carrying a...

Question 4

How much current must pass through a 400 turn coil 4.0 cm long to generate a 1.0-T magnetic field at the center?
A)0.013 A
B)13 A
C)22 A
D)40 A
E)80 A

Accepted Answer

The answer of How much current must pass through a...

Question 5

FIGURE 28-7 
-Two parallel segments of wire, of length L = 0.8m are positioned a distance d = 1 m apart as shown in Fig. 28-7. Calculate the magnetic field at point P located half-way between the two segments. (Each segment carries and electric current I = 10 A in the directions indicated.)
A)8 μT
B)3 μT
C)1 μT
D)0.5μT
E)0

Accepted Answer

The magnetic field at point P due to the left segment is equal in magnitude and opposite in direction to the magnetic field due to the right segment. Therefore, the net magnetic field at point P is zero.

Question 6

FIGURE 28-9 -Fig. 28-9 shows a segment of wire of length L = 0.5 m, carrying a current I = 20 A. Calculate the magnitude of the magnetic field produced by this wire at a point P located at a distance D = 1.0 m from one of the ends of the wire. A)0.8 × 10^-7 T B)5.8 × 10^-7 T C)2.1 × 10^-7 T D)6.3 × 10^-7 T E)8.9 × 10^-7 T

Accepted Answer

The answer of FIGURE 28-9 
-Fig. 28-9 shows a segment...

Question 7

A circular loop of wire of radius 10 cm carries a current of 6A. The magnitude of the magnetic field at the center of the loop is A)3.8 × 10^-5 T. B)3.8 × 10^-7 T. C)1.2 × 10^-5 T. D)1.2 × 10^-7 T. E)3.8 × 10^-8 T.

Accepted Answer

The magnetic field at the center of a circular loop is given by B = (μ₀I)/(2R). Using μ₀ = 4π × 10⁻⁷ Tm/A, I = 6 A, and R = 0.1 m, B = (4π × 10⁻⁷ × 6)/(2 × 0.1) = 3.8 × 10⁻⁵ T.

Question 8

FIGURE 28-8 -Fig. 28-8 shows the cross-section of a hollow cylinder of inner radius a = 5 cm and outer radius b = 7 cm. A uniform current density j = 1 A/ cm² flows through the cylinder. Calculate the magnitude of the magnetic field at a distance d = 10 cm from the axis of the cylinder. A)0 B)1.5 × 10^-4 T C)2.5 × 10^-4 T D)4.5 × 10^-4 T E)0.5 × 10^-4 T

Accepted Answer

The magnetic field outside a long cylindrical conductor with uniform current density can be calculated using Ampère's Law. The total current I through the cylinder is j times the cross-sectional area, which is π(b² - a²). Using Ampère's Law, B(2πd) = μ₀I, where d is the distance from the axis. Solving for B gives the magnitude of the magnetic field at d = 10 cm.

Question 9

What is the value of the magnetic field at the center of a square wire of length a on the side, if the current in the wire is I?
A)B = 
B)B = 
C)B = 
D)B = 
E)B = 0

Accepted Answer

The answer of What is the value of the magnetic...

Question 10

A toroidal solenoid has a radius R = 0.5 m and a cross-sectional diameter equal to 10 cm. When a current I passes through the coil of the solenoid, the magnetic field at the center of the solenoid has a magnitude B = 2 μT. What is the largest value of the magnetic field in the solenoid for the same value of the current?
A)3.5 μT
B)1.8 μT
C)2.2 μT
D)0.5 μT
E)2.8 μT

Accepted Answer

The answer of A toroidal solenoid has a radius R...

Question 11

A semicircular wire of radius R connects two straight wire segments. If a current I flows along the wire, the magnitude of the magnetic field at the center of the semicircular wire due to the current in the semicircular wire is A)μ_O I/2R. B)μ_O I/4R. C)μ_O I/8R. D)μ_O I/4πR. E)μ_O I/8πR.

Accepted Answer

The magnetic field at the center of a semicircular wire is given by B = (μ₀I)/(4R), derived from the Biot-Savart law for a circular arc.

Question 12

A wire of thickness d = 5 mm is tightly wound 200 times around a cylindrical core to form a solenoid. A current I = 0.1 A is sent through the wire. What is the the magnetic field on the axis of the solenoid? A)6.6 × 10^-5 T B)2.5 × 10^-5 T C)1.3 × 10^-5 T D)3.6 × 10^-5 T E)9.8 × 10^-5 T

Accepted Answer

The answer of A wire of thickness d = 5...

Question 13

A solenoid with a certain number of turns N and carrying a current of 2.000 A has a length of 34.00 cm. If the magnitude of the magnetic field generated at the center of the solenoid is 9.000 mT, what is the value of N?
A)860.0
B)1591
C)2318
D)3183
E)1218

Accepted Answer

The answer of A solenoid with a certain number of...

Question 14

A solenoid with 400 turns has a radius of 0.040 m and is 40 cm long. If this solenoid carries a current of 12 A, what is the magnitude of the magnetic field at the center of the solenoid?
A)16 mT
B)4.9 mT
C)15 mT
D)6.0 mT
E)9.0 mT

Accepted Answer

The magnetic field at the center of a solenoid is given by the formula:

B = μ₀ * n * I

Where μ₀ is the permeability of free space, n is the number of turns per unit length (n = N/L), and I is the current. Substituting the given values, we get:

n = N/L = 400 / 0.4 = 1000 turns/m
μ₀ = 4π x 10^-7 T m/A
I = 12 A

B = μ₀ * n * I = 4π x 10^-7 * 1000 * 12 = 15 mT

Therefore, the magnitude of the magnetic field at the center of the solenoid is 15 mT, which is closest to option C, 15 mT.

Question 15

FIGURE 28-10 -Two coaxial circular coils of radius R = 15 cm are positioned a distance d = 20 cm apart, as shown in Fig. 28-10. Calculate the magnetic field half-way between the coils. Each coil carries a current I = 4 A. A)0.9 × 10^-3 T B)3.9 × 10^-3 T C)1.9 × 10^-3 T D)6.3 × 10^-3 T E)9.2 × 10^-3 T

Accepted Answer

The magnetic field at the midpoint between two coaxial coils can be calculated using the Biot-Savart Law. For two identical coils, the fields add up. The formula for the magnetic field at the center of a single coil is B = (μ₀I)/(2R). At the midpoint, the field is half of this value for each coil, and since there are two coils, the total field is B = (μ₀I)/(2R). Substituting the given values, the correct answer is approximately 1.9 × 10⁻³ T.

Question 16

A straight wire carries a 12-A current eastward and a second straight wire carries a 14-A current westward. The wires are separated by a distance of 42 cm. The force on a 6.4 m length of one of the wires is A)8.0 × 10^-7 N. B)5.1 × 10^-4 N. C)8.0 × 10^-5 N. D)5.1 × 10^-6 N. E)not possible to determine with the information given.

Accepted Answer

The force between two parallel currents is given by F = (μ₀ * I₁ * I₂ * L) / (2π * d), where μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), I₁ and I₂ are the currents, L is the length of the wire, and d is the distance between the wires. Plugging in the values, F = (4π × 10⁻⁷ T·m/A * 12 A * 14 A * 6.4 m) / (2π * 0.42 m) = 5.1 × 10⁻⁴ N.

Question 17

How many turns should a 10-cm long solenoid have if it is to generate a 1.5 × 10^-³ T magnetic field on 1.0 A of current? A)12 B)15 C)120 D)1200 E)3200

Accepted Answer

The magnetic field inside a solenoid is given by:B = μ₀nIwhere:B is the magnetic field in teslasμ₀ is the permeability of free space (4π × 10^-7 T·m/A)n is the number of turns per unit length in turns/meterI is the current in amperesWe can rearrange this equation to solve for n:n = B / (μ₀I)Plugging in the given values, we get:n = (1.5 × 10^-3 T) / (4π × 10^-7 T·m/A * 1.0 A) = 120 turns/meterTo find the total number of turns, we multiply this by the length of the solenoid:N = nL = 120 turns/meter * 0.10 m = 120 turnsTherefore, the correct answer is C) 120.

Question 18

A 1000-turn toroid has a central radius of 4.2 cm and is carrying a current of 1.7 A. The magnitude of the magnetic field along the central radius is A)8.1 × 10^-3 T. B)5.1 × 10^-2 T. C)1.6 × 10^-2 T. D)8.1 × 10^-2 T. E)0.

Accepted Answer

The magnetic field inside a toroid is given by B = (μ₀ * N * I) / (2π * r), where N is the number of turns, I is the current, and r is the central radius. Substituting the given values, B = (4π × 10⁻⁷ T*m/A * 1000 * 1.7 A) / (2π * 0.042 m) = 8.1 × 10⁻³ T.

Question 19

FIGURE 28-6 
-Fig. 28-6 shows two long, parallel current-carrying wires. The wires carry equal currents  =  = 20 A in the directions indicated and are located a distance d = 0.5 m apart. Calculate the magnitude and direction of the magnetic field at a point located at an equal distance d from each wire.
A)8μT downward
B)8μT upward
C)4μT downward
D)4μT upward
E)4μT to the right

Accepted Answer

The answer of FIGURE 28-6 
-Fig. 28-6 shows two long,...

Question 20

Four long parallel wires each carry 2.0 A in the same direction. They are parallel to the z-axis, and they pass through the corners of a square of side 4.0 cm positioned in the x-y plane. What magnetic field does one of the wires experience due to the other wires? A)1.2 × 10^-⁶ T B)2.1 × 10^-⁶ T C)1.2 × 10^-⁵ T D)2.7 × 10^-⁵ T E)0 T

Accepted Answer

The answer of Four long parallel wires each carry 2.0...

Quiz 28: Sources of Magnetic Field

Two long parallel wires carry currents of 5.0 A and 8.0 A in the opposite direction. The wires are separated by 0.30 m. Find the magnetic force per unit length between the two wires.

A straight wire carries a 12-A current eastward and a second straight wire carries a 14-A current westward. The wires are separated by a distance of 42 cm. The force per unit length on the wire carrying 12 A is

A solenoid of 200 turns carrying a current of 2 A has a length of 25 cm. What is the magnitude of the magnetic field at the center of the solenoid?

How much current must pass through a 400 turn coil 4.0 cm long to generate a 1.0-T magnetic field at the center?

FIGURE 28-7 -Two parallel segments of wire, of length L = 0.8m are positioned a distance d = 1 m apart as shown in Fig. 28-7. Calculate the magnetic field at point P located half-way between the two segments. (Each segment carries and electric current I = 10 A in the directions indicated.)

FIGURE 28-9 -Fig. 28-9 shows a segment of wire of length L = 0.5 m, carrying a current I = 20 A. Calculate the magnitude of the magnetic field produced by this wire at a point P located at a distance D = 1.0 m from one of the ends of the wire.

A circular loop of wire of radius 10 cm carries a current of 6A. The magnitude of the magnetic field at the center of the loop is

FIGURE 28-8 -Fig. 28-8 shows the cross-section of a hollow cylinder of inner radius a = 5 cm and outer radius b = 7 cm. A uniform current density j = 1 A/ cm2 flows through the cylinder. Calculate the magnitude of the magnetic field at a distance d = 10 cm from the axis of the cylinder.

What is the value of the magnetic field at the center of a square wire of length a on the side, if the current in the wire is I?

A semicircular wire of radius R connects two straight wire segments. If a current I flows along the wire, the magnitude of the magnetic field at the center of the semicircular wire due to the current in the semicircular wire is

A wire of thickness d = 5 mm is tightly wound 200 times around a cylindrical core to form a solenoid. A current I = 0.1 A is sent through the wire. What is the the magnetic field on the axis of the solenoid?

A solenoid with a certain number of turns N and carrying a current of 2.000 A has a length of 34.00 cm. If the magnitude of the magnetic field generated at the center of the solenoid is 9.000 mT, what is the value of N?

A solenoid with 400 turns has a radius of 0.040 m and is 40 cm long. If this solenoid carries a current of 12 A, what is the magnitude of the magnetic field at the center of the solenoid?

FIGURE 28-10 -Two coaxial circular coils of radius R = 15 cm are positioned a distance d = 20 cm apart, as shown in Fig. 28-10. Calculate the magnetic field half-way between the coils. Each coil carries a current I = 4 A.

A straight wire carries a 12-A current eastward and a second straight wire carries a 14-A current westward. The wires are separated by a distance of 42 cm. The force on a 6.4 m length of one of the wires is

How many turns should a 10-cm long solenoid have if it is to generate a 1.5 × 10-3 T magnetic field on 1.0 A of current?

A 1000-turn toroid has a central radius of 4.2 cm and is carrying a current of 1.7 A. The magnitude of the magnetic field along the central radius is

Four long parallel wires each carry 2.0 A in the same direction. They are parallel to the z-axis, and they pass through the corners of a square of side 4.0 cm positioned in the x-y plane. What magnetic field does one of the wires experience due to the other wires?

FIGURE 28-8 -Fig. 28-8 shows the cross-section of a hollow cylinder of inner radius a = 5 cm and outer radius b = 7 cm. A uniform current density j = 1 A/ cm² flows through the cylinder. Calculate the magnitude of the magnetic field at a distance d = 10 cm from the axis of the cylinder.

How many turns should a 10-cm long solenoid have if it is to generate a 1.5 × 10^-³ T magnetic field on 1.0 A of current?