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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

Consider a model of the hydrogen atom in which an electron orbits a proton in the plane perpendicular to the proton's spin angular momentum (and magnetic dipole moment) at a distance equal to the Bohr radius, \(a_{0}=5.292 \cdot 10^{-11} \mathrm{~m} .\) (This is an oversimplified classical model.) The spin of the electron is allowed to be either parallel to the proton's spin or antiparallel to it; the orbit is the same in either case. But since the proton produces a magnetic field at the electron's location, and the electron has its own intrinsic magnetic dipole moment, the energy of the electron differs depending on its spin. The magnetic field produced by the proton's spin may be modeled as a dipole field, like the electric field due to an electric dipole discussed in Chapter 22 Calculate the energy difference between the two electronspin configurations. Consider only the interaction between the magnetic dipole moment associated with the electron's spin and the field produced by the proton's spin.

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.

28.39 The figure shows a cross section across the diameter of a long, solid, cylindrical conductor. The radius of the cylinder is \(R=10.0 \mathrm{~cm} .\) A current of \(1.35 \mathrm{~A}\) is uniformly distributed through the conductor and is flowing out of the page. Calculate the direction and the magnitude of the magnetic field at positions \(r_{\mathrm{a}}=0.0 \mathrm{~cm}\) \(r_{\mathrm{b}}=4.00 \mathrm{~cm}, r_{\mathrm{c}}=10.00 \mathrm{~cm}\) and \(r_{d}=16.0 \mathrm{~cm} .\)

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

Two long, parallel wires separated by a distance, \(d\), carry currents in opposite directions. If the left-hand wire carries a current \(i / 2,\) and the right-hand wire carries a current \(i\), determine where the magnetic field is zero.
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