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Chapter 28: Problem 1

Two long, straight wires are parallel to each other. The wires carry currents of different magnitudes. If the amount of current flowing in each wire is doubled, the magnitude of the force between the wires will be a) twice the magnitude of the original force. b) four times the magnitude of the original force. c) the same as the magnitude of the original force. d) half of the magnitude of the original force.

Short Answer

Expert verified
Answer: 4 times the magnitude of the original force.

Step by step solution

01

Write down the formula for the force between two parallel wires

The formula for the force between two parallel wires carrying currents I1 and I2 and separated by a distance d is given by: F = (mu_0 * I1 * I2 * l) / (2 * pi * d) where F is the force, mu_0 is the permeability of free space, and l is the length of the wires.
02

Analyze the change in currents

The currents in both wires are doubled. Let the new currents be I1_new and I2_new. We have: I1_new = 2 * I1 I2_new = 2 * I2
03

Write down the formula for the new force

Using the new currents, we can write the formula for the new force F_new as: F_new = (mu_0 * I1_new * I2_new * l) / (2 * pi * d)
04

Express the new force in terms of the old force

Substitute the new currents into the formula for F_new: F_new = (mu_0 * (2 * I1) * (2 * I2) * l) / (2 * pi * d) By simplifying this expression we get: F_new = 4 * (mu_0 * I1 * I2 * l) / (2 * pi * d) Since the original force is F = (mu_0 * I1 * I2 * l) / (2 * pi * d), we can write the new force as: F_new = 4 * F
05

Choose the appropriate option

The new force is four times the magnitude of the original force, so the correct answer is option (b).

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Most popular questions from this chapter

A circular wire of radius \(5.0 \mathrm{~cm}\) has a current of \(3.0 \mathrm{~A}\) flowing in it. The wire is placed in a uniform magnetic field of \(5.0 \mathrm{mT}.\) a) Determine the maximum torque on the wire. b) Determine the range of the magnetic potential energy of the wire.

A current of \(2.00 \mathrm{~A}\) is flowing through a 1000 -turn solenoid of length \(L=40.0 \mathrm{~cm} .\) What is the magnitude of the magnetic field inside the solenoid?

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A loop of wire of radius \(R=25.0 \mathrm{~cm}\) has a smaller loop of radius \(r=0.900 \mathrm{~cm}\) at its center such that the planes of the two loops are perpendicular to each other. When a current of \(14.0 \mathrm{~A}\) is passed through both loops, the smaller loop experiences a torque due to the magnetic field produced by the larger loop. Determine this torque assuming that the smaller loop is sufficiently small so that the magnetic field due to the larger loop is same across the entire surface.
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