Chapter 32, Problem 15SP

Figure 32-9(a) depicts a two-turn horizontal coil in a uniform downward B-field. Assume the field is increasing. (a) What is the direction of the induced magnetic field in the coil and why? (b) What is the direction of the induced current in the coil and why? (c) Which terminal is at a higher voltage? [Hint: Draw a diagram. Only concern yourself with what is happening inside the area of the coil.]

To determine

The direction of induced magnetic fieldin the two-turn horizontal coil when the magnetic field $B$ is directed downward andis increasing.

Answer to Problem 15SP

Solution:

Upward to oppose the downward increase.

Explanation of Solution

Introduction:

Lenz’s law:

When magnetic flux is passing through a coil, an emf is induced in the coil due to change in magnetic flux linked with the coil. The direction of the induced emf is so as to oppose the change.

Explanation:

The magnetic field $B$, that is directed downward, is increasing. Hence, according to Lenz’s law, the direction of magnetic field would be induced in the coil in such a way that it opposes the main magnetic flux.

Therefore, the direction of the induced magnetic field would be directed upward, as shown in figure (1).

In the figure (1), the symbol, $\odot$ represents the direction of the induced magnetic field $B_i$ along the upward direction in the coil.

Conclusion:

The induced magnetic field $B_i$, in the coil, should be directed upwards, opposite to the main increasing downward magnetic field.

To determine

The direction of induced current in a two-turn horizontal coil when the magnetic field $B$ is directed downward and is increasing.

Answer to Problem 15SP

Solution:

Counter clockwise direction.

Explanation of Solution

Introduction:

Lenz’s law:

When magnetic flux is passing through a coil, an emf is induced due to change in magnetic flux linked with the coil. The direction of induced emf is so as to oppose the change that produces it.

Explanation:

From part (a), the direction of induced magnetic field is upward, then the induced current $I_i$ in the coil would be in the anti-clockwise direction from $B\text{to }A$, because it produces the magnetic field $B_i$ upward, as shown in figure (2).

Conclusion:

The direction of induced current $I_i$ in the coil should be counter clockwise.

To determine

The higher voltage terminal in two-turn horizontal coil when the magnetic field

$B$, directed downward, is increasing.

Answer to Problem 15SP

Solution:

$V_A>V_B$

Explanation of Solution

Introduction:

The direction of current is always from negative terminal to the positive, inside the emf source, and positive terminal to the negative, outside the emf source.

Explanation:

The direction of induced magnetic field is upward, then the induced current $I_i$ in the coil flows in the anti-clockwise direction from $B\text{to }A$. Hence, the terminal A is positive and terminal B is negative. Hence, $V_A$ is higher than $V_B$ as shown in figure (3).

Conclusion:

$V_A$ is higher than $V_B$, or $V_A>V_B$.