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?

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.

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.

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.