Question 1

The magnetic field due to the current in a long, straight wire is 8.0 μT at a distance of 4.0 cm from the center of the wire. What is the current in the wire? (μ₀ = 4π × 10^-7 T ∙ m/A) A)0.20 A B)0.40 A C)0.80 A D)3.2 A E)1.6 A

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Question 2

A very long thin wire produces a magnetic field of $0.0020 \times 10 ^ { - 4 } \mathrm {~T}$ at a distance of $1.0 \mathrm {~mm}$ from the wire. What is the magnitude of the current? (?₀ = 4? × 10^-7 T ? m/A) A)1.0 mA B)2.0 mA C)4000 mA D)3100 mA

Accepted Answer

The magnitude of the current can be calculated using the formula for the magnetic field of a long, thin wire:$$B = \frac{\mu_0 I}{2\pi r}$$where:* B is the magnetic field strength* μ0 is the permeability of free space (4π × 10^-7 T ? m/A)* I is the current* r is the distance from the wirePlugging in the given values, we get:$$0.0020 	imes 10 ^ { - 4 } \mathrm {~T} = \frac{4\pi 	imes 10^{-7} \mathrm {~T~m/A} 	imes I}{2\pi 	imes 0.001 \mathrm {~m}}$$Solving for I, we get:$$I = 1.0 \mathrm {~mA}$$

Question 3

What is the strength of the magnetic field at the center of a circular loop of wire of diameter 8.0 cm when a current of 2.0 A flows in the wire? (?₀ = 4? × 10^-7 T ? m/A)

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Question 4

At a point 10 m away from a long straight thin wire, the magnetic field due to the wire is 0.10 mT. What current flows through the wire? (?₀ = 4? × 10^-7 T ? m/A)

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Question 5

How much current must flow through a long straight wire for the magnetic field strength to be 1.0 mT at 1.0 cm from a wire? (μ₀ = 4π × 10^-7 T ∙ m/A) A)50 mA B)9.2 A C)16 A D)50 A E)5.0 mA

Accepted Answer

Using the formula B = μ0I/2πr, we can solve for the current I:
I = 2πrB/μ0 = 2π(0.01 m)(1.0 × 10^-3 T)/(4π × 10^-7 T · m/A) ≈ 50 A. Therefore, the correct choice is D, 50 A.

Question 6

In the figure, the two long straight wires are separated by a distance of $d = 0.40 \mathrm {~m} .$ The currents are $I _ { 1 }$ = 1.0 A to the right in the upper wire and $I _ { 2 }$ = 8.0 A to the left in the lower wire. What are the magnitude and direction of the magnetic field at point P, that is a distance $d / 2 = 0.20 \mathrm {~m}$ below the lower wire? (?₀ = 4? × 10^-7 T ? m/A)

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Question 7

Three long parallel wires each carry 2.0-A currents in the same direction. The wires are oriented vertically, and they pass through three of the corners of a horizontal square of side 4.0 cm. What is the magnitude of the magnetic field at the fourth (unoccupied)corner of the square due to these wires? (μ₀ = 4π × 10^-7 T ∙ m/A) A)1.2 µT B)2.1 µT C)12 µT D)21 µT E)0 T

Accepted Answer

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Question 8

Two long parallel wires that are 0.40 m apart carry currents of 10 A in opposite directions. What is the magnetic field strength in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other? (μ₀ = 4π × 10^-7 T ∙ m/A) A)3.3 µT B)6.7 µT C)33 µT D)67 µT

Accepted Answer

The magnetic field at a point due to a long straight wire carrying current I is given by:
B = (μ0/2π) * (I/d)
where μ0 is the magnetic constant, d is the distance from the wire, and I is the current.
At the point 20 cm from one wire and 60 cm from the other, the magnetic field due to each wire can be calculated as follows:
B1 = (μ0/2π) * (10 A / 0.2 m) = 3.98 µT
B2 = (μ0/2π) * (10 A / 0.6 m) = 1.33 µT
Since the currents are in opposite directions, the net magnetic field at that point is:
Bnet = B1 - B2 = 2.65 µT (in the direction perpendicular to the wires)
Therefore, the best choice is B) 6.7 µT since it is the closest to the net magnetic field calculated above.

Question 9

Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 0.20 m. What is the strength of the magnetic field midway between the two wires? (μ₀ = 4π × 10^-7 T ∙ m/A) A)1.0 × 10^-5 T B)2.0 × 10^-5 T C)3.0 × 10^-5 T D)4.0 × 10^-5 T E)5.0 × 10^-5 T

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Question 10

Three very long, straight, parallel wires each carry currents of 4.0 A, directed out of the page as shown in the figure. These wires pass through the vertices of a right isosceles triangle as shown. Assume that all the quantities shown in the figure are accurate to two significant figures. What is the magnitude of the magnetic field at point P at the midpoint of the hypotenuse of the triangle? (μ₀ = 4π × 10^-7 T ∙ m/A) A)4.4 µT B)18 µT C)57 µT D)130 µT E)1.8 µT

Accepted Answer

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Question 11

The magnetic field at point P due to a 2.0-A current flowing in a long, straight, thin wire is 8.0 μT. How far is point P from the wire? (μ₀ = 4π × 10^-7 T ∙ m/A) A)2.0 cm B)2.5 cm C)4.0 cm D)5.0 cm E)10 cm

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Question 12

A flat circular wire loop of area 0.25 m² carries a current of 5.0 A. This coil lies on a horizontal table with the current flowing in the counterclockwise direction when viewed from above. At this point, the earth's magnetic field is 1.2 × 10^-5 T directed 60° below the horizontal. What is the magnitude of the torque that the earth's magnetic field exerts on this loop? A)2.5 × 10^-6 N ∙ m B)5.0 × 10^-6 N ∙ m C)7.5 × 10^-6 N ∙ m D)1.0 × 10^-5 N ∙ m

Accepted Answer

The torque on a wire loop in a magnetic field is given by:
τ = NABsinθ, 
where N is the number of turns, A is the area, B is the magnetic field, and θ is the angle between the magnetic field and the normal to the plane of the loop. Here, N = 1, A = 0.25 m^2, B = 1.2 × 10^-5 T, sinθ = sin(60°) = √3 / 2. Therefore, 
τ = (1)(0.25)(1.2 × 10^-5)(√3 / 2) = 7.5 × 10^-6 N∙m. 
So, the correct option is C.

Question 13

A long straight wire carrying a 4-A current is placed along the x-axis as shown in the figure. What is the magnitude of the magnetic field at a point P, located at y = 2 cm, due to the current in this wire? (μ₀ = 4π × 10^-7 T ∙ m/A) A)20 μT B)30 μT C)40 μT D)50 μT E)60 μT

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Question 14

A high power line carries a current of 1.0 kA. What is the strength of the magnetic field this line produces at the ground, 10 m away? (μ₀ = 4π × 10^-7 T ∙ m/A) A)4.7 µT B)6.4 µT C)20 µT D)56 µT

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Question 15

At what distance from a long straight wire carrying a current of 5.0 A is the magnitude of the magnetic field due to the wire equal to the strength of Earth's magnetic field of about 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T ∙ m/A) A)1.0 mm B)1.0 cm C)2.0 cm D)3.0 cm E)4.0 cm

Accepted Answer

We can use the formula for the magnetic field of a current-carrying wire at a distance $r$:

$$B=\frac{\mu_0 I}{2\pi r}$$

where $I$ is the current, $r$ is the distance from the wire, and $\mu_0$ is the permeability of free space.

We want to find the distance at which $B$ is equal to the strength of Earth's magnetic field $B_	ext{Earth}$, so we can set them equal to each other:

$$\frac{\mu_0 I}{2\pi r}=B_	ext{Earth}$$

Plugging in the given values:

$$\frac{4\pi	imes 10^{-7}	ext{ T}\cdot 	ext{m/A} 	imes 5.0	ext{ A}}{2\pi r}=5.0	imes 10^{-5}	ext{ T}$$

Simplifying:

$$r=\frac{4\pi	imes 10^{-7}	ext{ T}\cdot 	ext{m/A} 	imes 5.0	ext{ A}}{2\pi	imes 5.0	imes 10^{-5}	ext{ T}}=2.0	ext{ cm}$$

Therefore, the answer is (C) 2.0 cm.

Question 16

At point P the magnetic field due to a long straight wire carrying a current of 2.0 A is 1.2 µT. How far is P from the wire? (μ₀ = 4π × 10^-7 T ∙ m/A) A)11 cm B)22 cm C)33 cm D)44 cm E)55 cm

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Question 17

A flat square coil of wire measures 9.5 cm on each side and contains 175 turns of very thin wire. It carries a current of 6.3 A in a uniform 0.84-T magnetic field. What angle less than 90° should the plane of this coil make with the magnetic field direction so that the magnitude of the magnetic torque on it is 6.5 N ? m?

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Question 18

Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 20 cm. At what point between the two wires do they produce the same strength magnetic field?
A)4.0 cm from the 20 A wire
B)8.0 cm from the 20 A wire
C)12 cm from the 20 A wire
D)16 cm from the 20 A wire
E)18 cm from the 20 A wire

Accepted Answer

The magnetic field created by a current-carrying wire at a distance r from the wire is given by:

B = (μ₀/4π) x (I/r)

where I is the current, r is the distance, and μ₀ is the permeability of free space (4π x 10^-7 Tm/A).

For the 20 A wire, at a distance x from the wire, the magnetic field created is:

B1 = (μ₀/4π) x (20/x)

For the 5 A wire, at a distance 0.2 - x from the wire, the magnetic field created is:

B2 = (μ₀/4π) x (5/(0.2-x))

For the two wires to produce the same magnetic field at a point between them, we need:

B1 = B2

(μ₀/4π) x (20/x) = (μ₀/4π) x (5/(0.2-x))

Simplifying and solving for x, we get:

x = 0.16 m = 16 cm from the 20 A wire

Therefore, the answer is D: 16 cm from the 20 A wire.

Question 19

A long wire carrying a 2.0-A current is placed along the y-axis. What is the magnitude of the magnetic field at a point that is 0.60 m from the origin along the x-axis? (μ₀ = 4π × 10^-7 T ∙ m/A) A)0.67 µT B)1.3 µT C)0.12 µT D)6.7 T E)12 T

Accepted Answer

The magnitude of the magnetic field created by a long straight current-carrying wire at a distance $r$ from the wire is given by the formula $B = \frac{\mu_0 I}{2\pi r}$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}$, $I$ is the current, and $r$ is the distance from the wire. Plugging in the given values ($I = 2.0 \, \text{A}$ and $r = 0.60 \, \text{m}$), we get $B = \frac{4\pi \times 10^{-7} \times 2.0}{2\pi \times 0.60} = \frac{4 \times 10^{-7} \times 2.0}{1.2} = \frac{8 \times 10^{-7}}{1.2} = 6.67 \times 10^{-7} \, \text{T} = 0.67 \, \mu\text{T}$.

Question 20

The magnitude of the magnetic field that a long and extremely thin current-carrying wire produces at a distance of 3.0 µm from the center of the wire is 2.0 × 10^-3 T. How much current is flowing through the wire? (μ₀ = 4π × 10^-7 T ∙ m/A) A)30 mA B)190 mA C)19 mA D)380 mA

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Quiz 24: Magnetic Fields and Forces

The magnetic field due to the current in a long, straight wire is 8.0 μT at a distance of 4.0 cm from the center of the wire. What is the current in the wire? (μ0 = 4π × 10-7 T ∙ m/A)

A very long thin wire produces a magnetic field of 0.0020×10−4 T0.0020 \times 10 ^ { - 4 } \mathrm {~T}0.0020×10−4 T at a distance of 1.0 mm1.0 \mathrm {~mm}1.0 mm from the wire. What is the magnitude of the current? (?0 = 4? × 10-7 T ? m/A)

What is the strength of the magnetic field at the center of a circular loop of wire of diameter 8.0 cm when a current of 2.0 A flows in the wire? (?0 = 4? × 10-7 T ? m/A)

At a point 10 m away from a long straight thin wire, the magnetic field due to the wire is 0.10 mT. What current flows through the wire? (?0 = 4? × 10-7 T ? m/A)

How much current must flow through a long straight wire for the magnetic field strength to be 1.0 mT at 1.0 cm from a wire? (μ0 = 4π × 10-7 T ∙ m/A)

Two long parallel wires that are 0.40 m apart carry currents of 10 A in opposite directions. What is the magnetic field strength in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other? (μ0 = 4π × 10-7 T ∙ m/A)

Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 0.20 m. What is the strength of the magnetic field midway between the two wires? (μ0 = 4π × 10-7 T ∙ m/A)

The magnetic field at point P due to a 2.0-A current flowing in a long, straight, thin wire is 8.0 μT. How far is point P from the wire? (μ0 = 4π × 10-7 T ∙ m/A)

A long straight wire carrying a 4-A current is placed along the x-axis as shown in the figure. What is the magnitude of the magnetic field at a point P, located at y = 2 cm, due to the current in this wire? (μ0 = 4π × 10-7 T ∙ m/A)

A high power line carries a current of 1.0 kA. What is the strength of the magnetic field this line produces at the ground, 10 m away? (μ0 = 4π × 10-7 T ∙ m/A)

At what distance from a long straight wire carrying a current of 5.0 A is the magnitude of the magnetic field due to the wire equal to the strength of Earth's magnetic field of about 5.0 × 10-5 T? (μ0 = 4π × 10-7 T ∙ m/A)

At point P the magnetic field due to a long straight wire carrying a current of 2.0 A is 1.2 µT. How far is P from the wire? (μ0 = 4π × 10-7 T ∙ m/A)

Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 20 cm. At what point between the two wires do they produce the same strength magnetic field?

A long wire carrying a 2.0-A current is placed along the y-axis. What is the magnitude of the magnetic field at a point that is 0.60 m from the origin along the x-axis? (μ0 = 4π × 10-7 T ∙ m/A)

The magnitude of the magnetic field that a long and extremely thin current-carrying wire produces at a distance of 3.0 µm from the center of the wire is 2.0 × 10-3 T. How much current is flowing through the wire? (μ0 = 4π × 10-7 T ∙ m/A)

The magnetic field due to the current in a long, straight wire is 8.0 μT at a distance of 4.0 cm from the center of the wire. What is the current in the wire? (μ₀ = 4π × 10^-7 T ∙ m/A)

A very long thin wire produces a magnetic field of $0.0020 \times 10 ^ { - 4 } \mathrm {~T}$ at a distance of $1.0 \mathrm {~mm}$ from the wire. What is the magnitude of the current? (?₀ = 4? × 10^-7 T ? m/A)

What is the strength of the magnetic field at the center of a circular loop of wire of diameter 8.0 cm when a current of 2.0 A flows in the wire? (?₀ = 4? × 10^-7 T ? m/A)

At a point 10 m away from a long straight thin wire, the magnetic field due to the wire is 0.10 mT. What current flows through the wire? (?₀ = 4? × 10^-7 T ? m/A)

How much current must flow through a long straight wire for the magnetic field strength to be 1.0 mT at 1.0 cm from a wire? (μ₀ = 4π × 10^-7 T ∙ m/A)

Two long parallel wires that are 0.40 m apart carry currents of 10 A in opposite directions. What is the magnetic field strength in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other? (μ₀ = 4π × 10^-7 T ∙ m/A)

Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 0.20 m. What is the strength of the magnetic field midway between the two wires? (μ₀ = 4π × 10^-7 T ∙ m/A)

The magnetic field at point P due to a 2.0-A current flowing in a long, straight, thin wire is 8.0 μT. How far is point P from the wire? (μ₀ = 4π × 10^-7 T ∙ m/A)

A long straight wire carrying a 4-A current is placed along the x-axis as shown in the figure. What is the magnitude of the magnetic field at a point P, located at y = 2 cm, due to the current in this wire? (μ₀ = 4π × 10^-7 T ∙ m/A)

A high power line carries a current of 1.0 kA. What is the strength of the magnetic field this line produces at the ground, 10 m away? (μ₀ = 4π × 10^-7 T ∙ m/A)

At what distance from a long straight wire carrying a current of 5.0 A is the magnitude of the magnetic field due to the wire equal to the strength of Earth's magnetic field of about 5.0 × 10^-5 T? (μ₀ = 4π × 10^-7 T ∙ m/A)

At point P the magnetic field due to a long straight wire carrying a current of 2.0 A is 1.2 µT. How far is P from the wire? (μ₀ = 4π × 10^-7 T ∙ m/A)

A long wire carrying a 2.0-A current is placed along the y-axis. What is the magnitude of the magnetic field at a point that is 0.60 m from the origin along the x-axis? (μ₀ = 4π × 10^-7 T ∙ m/A)

The magnitude of the magnetic field that a long and extremely thin current-carrying wire produces at a distance of 3.0 µm from the center of the wire is 2.0 × 10^-3 T. How much current is flowing through the wire? (μ₀ = 4π × 10^-7 T ∙ m/A)