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Chapter 28: Problem 5

In a solenoid in which the wires are wound such that each loop touches the adjacent ones, which of the following will increase the magnetic field inside the magnet? a) making the radius of the loops smaller b) increasing the radius of the wire c) increasing the radius of the solenoid d) decreasing the radius of the wire e) immersion of the solenoid in gasoline

Short Answer

Expert verified
Answer: Decreasing the radius of the wire.

Step by step solution

01

Analyze option (a)

Making the radius of the loops smaller will not increase the number of turns per unit length or the current flowing through the wire. Therefore, this option will not increase the magnetic field inside the magnet.
02

Analyze option (b)

Increasing the radius of the wire will increase the resistance of the wire (R = ρ * (L/A), where ρ is the resistivity, A is the cross-sectional area). This will decrease the current flowing through the wire, which will not increase the magnetic field inside the magnet.
03

Analyze option (c)

Increasing the radius of the solenoid will not change the number of turns per unit length or the current flowing through the wire. Thus, this option will not increase the magnetic field inside the magnet.
04

Analyze option (d)

Decreasing the radius of the wire will decrease the resistance of the wire. This will increase the current flowing through the wire, which will increase the magnetic field inside the magnet. Therefore, option (d) is correct.
05

Analyze option (e)

Immersion of the solenoid in gasoline has no direct effect on the number of turns per unit length or the current flowing through the wire. Therefore, this option will not increase the magnetic field inside the magnet. In conclusion, the correct answer is option (d) - decreasing the radius of the wire will increase the magnetic field inside the magnet.

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Most popular questions from this chapter

Consider an electron to be a uniformly dense sphere of charge, with a total charge of \(-e=-1.60 \cdot 10^{-19} \mathrm{C}\) spinning at an angular frequency, \(\omega\). a) Write an expression for its classical angular momentum of rotation, \(L\) b) Write an expression for its magnetic dipole moment, \(\mu\). c) Find the ratio, \(\gamma_{e}=\mu / L\), known as the gyromagnetic ratio.

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 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.

Discuss how the accuracy of a compass needle in showing the true direction of north can be affected by the magnetic field due to currents in wires and appliances in a residential building.

Two particles, each with charge \(q\) and mass \(m\), are traveling in a vacuum on parallel trajectories a distance \(d\) apart, both at speed \(v\) (much less than the speed of light). Calculate the ratio of the magnitude of the magnetic force that each exerts on the other to the magnitude of the electric force that each exerts on the other: \(F_{\mathrm{m}} / \mathrm{F}_{\mathrm{e}}\)
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