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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 current of constant density, \(J_{0}\), flows through a very long cylindrical conducting shell with inner radius \(a\) and outer radius \(b\). What is the magnetic field in the regions \(rb\) ? Does \(B_{ab}\) for \(r=b\) ?

A long, straight wire carries a current of 2.5 A. a) What is the strength of the magnetic field at a distance of \(3.9 \mathrm{~cm}\) from the wire? b) If the wire still carries \(2.5 \mathrm{~A}\), but is used to form a long solenoid with 32 turns per centimeter and a radius of \(3.9 \mathrm{~cm}\) what is the strength of the magnetic field at the center of the solenoid?

If you want to construct an electromagnet by running a current of 3.0 A through a solenoid with 500 windings and length \(3.5 \mathrm{~cm}\) and you want the magnetic field inside the solenoid to have magnitude \(B=2.96 \mathrm{~T}\), you can insert a ferrite core into the solenoid. What value of the relative magnetic permeability should this ferrite core have in order to make this work?

A long, straight wire is located along the \(x\) -axis \((y=0\) and \(z=0)\). The wire carries a current of \(7.00 \mathrm{~A}\) in the positive \(x\) -direction. What is the magnitude and the direction of the force on a particle with a charge of 9.00 C located at \((+1.00 \mathrm{~m},+2.00 \mathrm{~m}, 0),\) when it has a velocity of \(3000 . \mathrm{m} / \mathrm{s}\) in each of the following directions? a) the positive \(x\) -direction c) the negative \(z\) -direction b) the positive \(y\) -direction

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