Physics for Scientists and Engineers, 6e

Chapter 30 – Sources of the Magnetic Field

Consider the current in the length of wire shown in the figure below. Rank the points A, B, and C, in terms of magnitude of the magnetic field due to the current in the length element shown, from greatest to least.

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1. A, B, C

2. B, C, A

3. C, B, A

4. C, A, B

5. An equal field applies at all these points.

Point B is closest to the current element. Point C is farther away and the field is further reduced by the sin θ factor in the cross product ds × . The field at A is zero because θ = 0.

For I1 = 2 A and I2 = 6 A in the figure below, which is

true:

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1. F1 = 3F2

2. F1 = F2/3

3. F1 = F2

F1 = F2 as required by Newton’s third law.

Another way to arrive at this answer is to realize that Equation 30.11 gives the same result whether the multiplication of currents is (2 A)(6 A) or (6 A)(2 A).

A loose spiral spring is hung from the ceiling, and a large current is sent through it. The coils move

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1. closer together

2. farther apart

3. they do not move at all

The coils act like wires carrying parallel currents in the same direction and hence attract one another.

Rank the magnitudes of B · ds for the closed paths in the figure below, from least to greatest.

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1. a, b, c, d

2. b, d, a, c

3. c, d, b, a

4. c, b, a, d

5. d, c, a, b

Equation 30.13 indicates that the value of the line integral depends only on the net current through each closed path. Path b encloses 1 A, path d encloses 3 A, path a encloses 4 A, and path c encloses 6 A.

Rank the magnitudes of B · ds for the closed paths in the figure below, from least to greatest.

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1. a, b, c, d

2. b, c, d, a

3. b, d, a, c

4. d, c, a, b

5. The criteria is badly chosen in this case

Ranked from least to greatest, first comes b, then a = c = d. Paths a, c, and d all give the same nonzero value μ0I because the size

and shape of the paths do not matter. Path b does not enclose the current, and hence its line integral is zero.

Consider a solenoid that is very long compared to the radius. Of the following choices, the most effective way to increase the magnetic field in the interior of the solenoid is:

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1. double its length, keeping the number of turns per unit length constant

2. reduce its radius by half, keeping the number of turns per unit length constant

3. overwrapping the entire solenoid with an additional layer of current-carrying wire

The magnetic field in a very long solenoid is independent of its length or radius. Overwrapping with an additional layer of wire increases the number of turns per unit length.

In an RC circuit, the capacitor begins to discharge. During the discharge, in the region of space between the plates of the capacitor, there is

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1. conduction current but no displacement current

2. displacement current but no conduction current

3. both conduction and displacement current

4. no current of any type

There can be no conduction current because there is no conductor between the plates. There is a time-varying electric field because of the decreasing charge on the plates, and the time-varying electric flux represents a displacement current.

The capacitor in an RC circuit begins to discharge. During the discharge, in the region of space between the plates of the capacitor, there is

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1. an electric field but no magnetic field

2. a magnetic field but no electric field

3. both electric and magnetic fields

4. no fields of any type

There is a time-varying electric field because of the decreasing charge on the plates. This time-varying electric field produces a magnetic field.

Which material would make a better permanent magnet?

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1. one whose hysteresis loop looks like Figure (a)

2. one whose hysteresis loop looks like Figure (b)

The loop that looks like Figure 30.32a is better because the remanent magnetization at the point corresponding to point b in Figure 30.31 is greater.

If we wanted to cancel the Earth’s magnetic field by running an enormous current loop around the equator, the current loop would be directed:

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1. east to west

2. west to east

The lines of the Earth’s magnetic field enter the planet in Hudson Bay and emerge from Antarctica; thus, the field lines resulting from the current would have to go in the opposite direction. Compare Figure 30.7a with Figure 30.36