Question 1

A long straight wire carries a current $$i_1$$ and a rectangular loop a distance $$a$$ away, with sides of length $$b$$ and $$c$$, carries a current $$i_2. $$According to the right-hand rule, in which direction does the force on the segment of the loop parallel to the wire (at distance $$a) $$act?

Accepted Answer

Toward the wire

Question 2

Given the same setup, what is the direction of the force on the segment of the loop parallel to the wire but at distance $$a + b$$ from the wire?

Accepted Answer

Away from the wire

Question 3

What is the net force on the rectangular loop due to the current $$i_1 in $$the straight wire, in terms of $$a$$ and $$b$$?

Accepted Answer

$$F = \frac{\mu_0$ i_1$ i_2$ c}{2\pi} \left( \frac{1}{a} - \frac{1}{a+b} \right)$$

Question 4

Using Ampère’s law, what is the expression for the magnetic field at the center of a long solenoid of length $$\ell$$, with $$N$$ turns and current $$I$$?

Accepted Answer

$$B = \mu_0$ \frac{N}{\ell} I$$

Question 5

A solenoid has 1000 turns uniformly distributed over a length of 40.0 cm. What current is needed to produce a magnetic field of $$1.00 	imes 10$$^{-4}$$ T at its center?

Accepted Answer

$$I = 3.18 \ \mathrm{A}$$

Question 6

For a solenoid, the inductance $$L is $$given by $$L = \frac{N \Phi_B}{I}. $$What does $$L$$ physically represent?

Accepted Answer

The inductance, which measures the solenoid's ability to store energy in its magnetic field

Question 7

What additional physical property of the coil is needed to determine $$L$$ for the solenoid described above?

Accepted Answer

The cross-sectional area of the coil

Question 8

If the current in the solenoid is doubled, what happens to the magnetic field at its center?

Accepted Answer

It doubles

Question 9

Which of the following best describes the force between two parallel currents in the same direction?

Accepted Answer

They attract each other

Question 10

A rectangular loop is placed near a long straight wire carrying current $$i_1. If $$the current in the wire is reversed, what happens to the direction of the net force on the loop?

Accepted Answer

The direction of the net force reverses

Question 11

Which equation correctly gives the inductance $$L of a $$solenoid in terms of its physical properties?

Accepted Answer

$$L = \mu_0$ \frac{N^2$ A}{\ell}$$

Question 12

If the length of a solenoid is doubled while keeping the number of turns and current constant, what happens to the magnetic field at its center?

Accepted Answer

It is halved

Question 13

A rectangular loop carrying current $$i_2 is $$placed near a long straight wire carrying current $$i_1. If $$the distance $$a is $$decreased, what happens to the magnitude of the net force on the loop?

Accepted Answer

It increases

Question 14

Which of the following is a correct application of Ampère’s law for a long solenoid?

Accepted Answer

$$\oint \vec{B} \cdot d\vec{l} = \mu_0$ N I$$

Magnetic Forces on a Current Loop and Solenoid Properties

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