Question

Figure 30-31 shows three situations in which a wire loop lies partially in a magnetic field.The magnitude of the field is either increasing or decreasing, as indicated. In each situation, a battery is part of the loop. In which situations are the induced emf and the battery emf in the same direction along the loop?

Short answer

In situation (b), the induced emf and the battery emf in the same direction along the loop.

Step-by-step solution

Step 1: Given

1. Fig.30-31.
2. A wire loop lies partially in a magnetic field.
3. In this situation, the battery is a part of the loop.

Determining the concept

Applying Lenz’s law in given Fig.30-31, find the induced current ${\mathit{i}}_{\mathbf{i}\mathbf{n}\mathbf{d}}$ and comparing it with the direction of the current ${\mathit{i}}_{\mathbf{b}\mathbf{a}\mathbf{t}}$ from the battery, find in which situations, the induced emf and the battery emf in the same direction along the loop.

Formulae are as follow:

$E_{emf}=‐N\frac{d\varnothing }{dt}$

Where,

E = induced emf.

$d\varnothing$= change in magnetic flux.

N = number of turns in coil.

dt = change in time.

Determining the situations in which, the induced emf and the battery emf are in the same direction along the loop

Lenz’s law gives direction of induced current. From Fig.30-5, the direction of the induced current in various conditions.

Applying Lenz’s law in Fig.30-31(a), the direction of induced current$i_{ind}$isclockwisebut the direction of current from the battery$i_{bat}$iscounterclockwise.

Applying Lenz’s law in Fig.30-31(b), the direction of induced current$i_{ind}$isclockwisebut the direction of current from the battery$i_{bat}$is alsoclockwise.

Applying Lenz’s law in Fig.30-31(c), the direction of induced current$i_{ind}$is counterclockwise but the direction of current from the battery$i_{bat}$is clockwise.

Therefore, in (b) situation, the induced emf and the battery emf are in the same direction along the loop.

Using Lenz’s law, answer this question.