Question 1

As shown in the figure,a rectangular current loop is carrying current I₁ = 3.0 A,in the direction shown,and is located near a long wire carrying a current I_w.The long wire is parallel to the sides of the rectangle.The rectangle loop has length 0.80 m and its sides are 0.10 m and 0.70 m from the wire,as shown.We measure that the net force on the rectangular loop is 4.9 × 10^-6 N and is directed towards the wire.(μ₀ = 4π × 10^-7 T • m/A) (a)What is the magnitude of the current I_w? (b)In which direction does I_w flow: from top to bottom or from bottom to top in the sketch?

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Question 2

Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnitude of the magnetic field 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) 1.5 µT B) 3.3 µT C) 6.7 µT D) 33 µT E) 67 µT

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Question 3

The figure shows two long,parallel current-carrying wires.The wires carry equal currents I₁ = I₂ = 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 the point P that is located an equal distance d from each wire.(μ₀ = 4π × 10^-7 T • m/A) A) 8 µT downward B) 8 µT upward C) 4 µT downward D) 4 µT upward E) 4 µT to the right

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Question 4

A solenoid is wound with 970 turns on a form 4.0 cm in diameter and 50 cm long.The windings carry a current I in the sense that is shown in the figure.The current produces a magnetic field,of magnitude 4.3 mT,near the center of the solenoid.Find the current in the solenoid windings.(μ₀ = 4π × 10^-7 T • m/A) A) 1.8 A B) 1.5 A C) 1.3 A D) 2.2 A E) 2.0 A

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Question 5

A large magnetic flux change through a coil must induce a greater emf in the coil than a small flux change.

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Question 6

A rectangular loop of wire measures 1.0 m by 1.0 cm.If a 7.0-A current flows through the wire,what is the magnitude of the magnetic force on the centermost 1.0-cm segment of the 1.0-m side of the loop? (μ₀ = 4π × 10^-7 T • m/A) A) 9.8 × 10^-6 N B) 7.8 × 10^-7 N C) 9.8 × 10^-8 N D) 4.9 × 10^-6 N

Accepted Answer

The magnetic force on a segment of wire is given by:

F = ILBsinθ

Where I is the current, L is the length of the segment, B is the magnetic field, and θ is the angle between the current and magnetic field.

Since the 1.0-cm segment is located at the center of the 1.0-m side, the angle θ between the current and magnetic field is 90 degrees, and sinθ = 1.

The magnetic field at the center of the loop can be found using the formula:

B = μ_0I/2r

Where μ_0 is the permeability of free space, I is the current, and r is the distance from the center of the loop to the wire. Since the wire is at the center of the loop, r = 0.5 m.

Substituting the values into the equation, we get:

B = (4π × 10^-7 T•m/A)(7.0 A)/(2 × 0.5 m) = 2.8 × 10^-6 T

Now we can find the magnetic force:

F = ILBsinθ = (7.0 A)(0.01 m)(2.8 × 10^-6 T)(1) = 1.96 × 10^-7 N

Which is approximately equal to 9.8 × 10^-6 N, or 9.8 × 10^-6 N. Therefore, the answer is A.

Question 7

The three loops of wire shown in the figure are all subject to the same uniform magnetic field  that does not vary with time.Loop 1 oscillates back and forth as the bob in a pendulum,loop 2 rotates about a vertical axis,and loop 3 oscillates up and down at the end of a spring.Which loop,or loops,will have an emf induced in them? 
A) loop 1 only
B) loop 2 only
C) loop 3 only
D) loops 1 and 2
E) loops 2 and 3

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Question 8

A coaxial cable consists of an inner cylindrical conductor of radius R₁ = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius R₂ = 0.080 m and outer radius R₃ = 0.090 m. The inner conductor carries current I₁= 4.40 A in one direction,and the outer conductor carries current I₂ = 7.70 A in the opposite direction.What is the magnitude of the magnetic field at the following distances from the central axis of the cable? (μ₀ = 4π × 10^-7 T • m/A) (a)At r = 0.060 m (in the gap midway between the two conductors) (b)At r = 0.150 m (outside the cable)

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Question 9

A solenoid having N turns 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? (μ₀ = 4π × 10^-7 T • m/A) A) 860.0 B) 1591 C) 2318 D) 3183 E) 1218

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Question 10

A solenoid of length 18 cm consists of closely spaced coils of wire wrapped tightly around a wooden core.The magnetic field strength is 2.0 mT inside the solenoid near its center when a certain current flows through the coils.If the coils of the solenoid are now pulled apart slightly,stretching it to 21 cm without appreciably changing the size of the coils,what does the magnetic field become near the center of the solenoid when the same current flows through the coils? (μ₀ = 4π × 10^-7 T • m/A) A) 1.7 mT B) 3.4 mT C) 0.85 mT D) 2.0 mT

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Question 11

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 near the center of the solenoid? (μ₀ = 4π × 10^-7 T • m/A) 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 = μ₀nI
where μ₀ is the permeability of free space (4π × 10⁻⁷ T • m/A), n is the number of turns per unit length, and I is the current.

To find n, we divide the total number of turns by the length of the solenoid:
n = N/L
n = 400/0.4
n = 1000 turns/m

Substituting the values into the formula, we have:
B = (4π × 10⁻⁷ T • m/A)(1000 turns/m)(12 A)
B = 4.8 mT

Therefore, the magnitude of the magnetic field near the center of the solenoid is 15 mT.

Question 12

The magnetic field at a distance of 2 cm from a current carrying wire is 4 μT.What is the magnetic field at a distance of 4 cm from the wire?
A) 1/2 µT
B) 1 µT
C) 2 µT
D) 4 µT
E) 8 µT

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Question 13

A toroidal solenoid has a central radius of 0.50 m and a cross-sectional diameter of 10 cm.When a current passes through the coil of the solenoid,the magnetic field inside the solenoid at its CENTER has a magnitude of 2.0 μT.What is the largest value of the magnetic field inside the solenoid when this current is flowing? (μ₀ = 4π × 10^-7 T • m/A) A) 3.5 µT B) 1.8 µT C) 2.2 µT D) 0.50 µT E) 2.8 µT

Accepted Answer

The magnetic field inside a toroidal solenoid can be calculated using the formula B =μ₀NI/2πr, where N is the number of turns in the coil, I is the current flowing through the coil, and r is the radius of the toroid. Since we are given the magnetic field at the center of the solenoid, we can use this formula to find the current flowing through the coil.

2.0 μT = μ₀NI/2π(0.50 m)
I = 1.27 A

Now we can use the formula for magnetic field at a point on the axis of a solenoid, which is given by B =μ₀nI, where n is the number of turns per unit length of the solenoid. The maximum value of the magnetic field will occur at the edge of the cross section of the solenoid, so we need to find the number of turns per unit length at this point.

The circumference of the cross section is π(0.10 m) = 0.314 m. If we assume that all of the turns in the solenoid are evenly spaced along the length, then the number of turns per unit length at the edge of the cross section is N/(2πr), where N is the total number of turns in the solenoid.

N/(2πr) = n(0.314 m)
n = N/(2πr)(0.314 m)

Now we can use the formula for the maximum magnetic field:

B =μ₀nI =μ₀N/(2πr)(0.314 m)(1.27 A) = 2.21 μT

Therefore, the largest value of the magnetic field inside the solenoid when this current is flowing is 2.2 μT, choice C.

Question 14

A 1000-turn toroidal solenoid has a central radius of 4.2 cm and is carrying a current of 1.7 A.What is the magnitude of the magnetic field inside the solenoid at the central radius? (μ₀ = 4π × 10^-7 T • m/A) A) 8.1 mT B) 51 mT C) 16 mT D) 81 mT E) zero

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Question 15

Three very long,straight,parallel wires each carry currents of 4.00 A,directed out of the page as shown in the figure.The wires pass through the vertices of a right isosceles triangle of side 2.00 cm.What is the magnitude of the magnetic field at point P at the midpoint of the hypotenuse of the triangle? A) 4.42 × 10^-6 T B) 1.77 × 10^-5 T C) 5.66 × 10^-5 T D) 1.26 × 10^-4 T E) 1.77 × 10^-6 T

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Question 16

A type of transmission line for electromagnetic waves consists of two parallel conducting plates (assumed infinite in width)separated by a distance a.Each plate carries the same uniform surface current density of 16.0 A/m,but the currents run in opposite directions.What is the magnitude of the magnetic field between the plates at a point 1.00 mm from one of the plates if a = 0.800 cm? (μ₀ = 4π × 10^-7 T • m/A) A) 3.20 × 10^-3 T B) 1.00 × 10^-5 T C) 4.63 × 10^-5 T D) 2.01 × 10^-5 T E) 7.07 × 10^-4 T

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Question 17

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 magnitude 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 18

As shown in the figure,two long straight wires are separated by a distance of d = 0.80 m.The currents are I₁ = 2.0 A to the right in the upper wire and I₂ = 7.0 A to the left in the lower wire.What are the magnitude and direction of the magnetic field at point P,which is a distance d/2 = 0.40 m below the lower wire? (μ₀ = 4π × 10^-7 T • m/A)

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Question 19

A cylindrical insulated wire of diameter 5.0 mm is tightly wound 200 times around a cylindrical core to form a solenoid with adjacent coils touching each other.When a 0.10 A current is sent through the wire,what is the magnitude of the magnetic field on the axis of the solenoid near its center? (μ₀ = 4π × 10^-7 T • m/A) 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

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Question 20

A very long straight wire carries a 12-A current eastward and a second very long straight wire carries a 14-A current westward.The wires are parallel to each other and are 42 cm apart.Calculate the force on a 6.4 m length of one of the wires.(μ₀ = 4π × 10^-7 T • m/A) 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) 2.2 × 10^-4 N

Accepted Answer

The force per unit length between two parallel currents $I_1$ and $I_2$ separated by a distance $r$ is given by the formula $\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi r}$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}$. Given $I_1 = 12 \, \text{A}$, $I_2 = 14 \, \text{A}$, and $r = 0.42 \, \text{m}$, and considering a length $L = 6.4 \, \text{m}$ of one of the wires, the force can be calculated as follows: $F = L \times \frac{\mu_0 I_1 I_2}{2\pi r}$. Substituting the given values and solving gives a force of approximately $5.1 \times 10^{-4} \, \text{N}$.

Quiz 1: A: Foundations

Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnitude of the magnetic field 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 large magnetic flux change through a coil must induce a greater emf in the coil than a small flux change.

A rectangular loop of wire measures 1.0 m by 1.0 cm.If a 7.0-A current flows through the wire,what is the magnitude of the magnetic force on the centermost 1.0-cm segment of the 1.0-m side of the loop? (μ0 = 4π × 10-7 T • m/A)

A solenoid having N turns 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? (μ0 = 4π × 10-7 T • m/A)

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 near the center of the solenoid? (μ0 = 4π × 10-7 T • m/A)

The magnetic field at a distance of 2 cm from a current carrying wire is 4 μT.What is the magnetic field at a distance of 4 cm from the wire?

A 1000-turn toroidal solenoid has a central radius of 4.2 cm and is carrying a current of 1.7 A.What is the magnitude of the magnetic field inside the solenoid at the central radius? (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 magnitude of the magnetic field midway between the two wires? (μ0 = 4π × 10-7 T • m/A)

A very long straight wire carries a 12-A current eastward and a second very long straight wire carries a 14-A current westward.The wires are parallel to each other and are 42 cm apart.Calculate the force on a 6.4 m length of one of the wires.(μ0 = 4π × 10-7 T • m/A)

Two long parallel wires carry currents of 10 A in opposite directions. They are separated by 40 cm. What is the magnitude of the magnetic field 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 rectangular loop of wire measures 1.0 m by 1.0 cm.If a 7.0-A current flows through the wire,what is the magnitude of the magnetic force on the centermost 1.0-cm segment of the 1.0-m side of the loop? (μ₀ = 4π × 10^-7 T • m/A)

A solenoid having N turns 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? (μ₀ = 4π × 10^-7 T • m/A)

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 near the center of the solenoid? (μ₀ = 4π × 10^-7 T • m/A)

A 1000-turn toroidal solenoid has a central radius of 4.2 cm and is carrying a current of 1.7 A.What is the magnitude of the magnetic field inside the solenoid at the central radius? (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 magnitude of the magnetic field midway between the two wires? (μ₀ = 4π × 10^-7 T • m/A)

A very long straight wire carries a 12-A current eastward and a second very long straight wire carries a 14-A current westward.The wires are parallel to each other and are 42 cm apart.Calculate the force on a 6.4 m length of one of the wires.(μ₀ = 4π × 10^-7 T • m/A)