Question

Three identical coils $C_1$, $C_2$ and $C_3$ are closely placed such that they share a common axis. $C_2$ is exactly midway. $C_1$ carries current $I$ in anti-clockwise direction while $C_3$ carries current $I$ in clockwise direction. An induced current flows through $C_2$ will be in clockwise direction when

• A. $C_1$ and $C_3$ move with equal speeds away from $C_2$
• B. $C_1$ moves away from $C_2$ and $C_3$ moves towards $C_2$
• C. $C_1$ moves towards $C_2$ and $C_3$ moves away from $C_2$
• D. $C_1$ and $C_3$ move with equal speeds towards $C_2$

Hint:

Always apply Lenz’s law by first deciding whether magnetic flux is increasing or decreasing, then choose the induced current direction to oppose that change.

Answer 1

The Correct Option is C

Step 1: Determine magnetic field directions.
- $C_1$ carries current in anti-clockwise direction, so its magnetic field at $C_2$ is out of the plane.
- $C_3$ carries current in clockwise direction, so its magnetic field at $C_2$ is also out of the plane.
Thus, both coils produce magnetic flux in the same direction through $C_2$.
Step 2: Apply Lenz's law.
According to Lenz’s law, the induced current opposes the change in magnetic flux.
Step 3: Analyze option (C).
- $C_1$ moves towards $C_2$: magnetic flux through $C_2$ increases.
- $C_3$ moves away from $C_2$: magnetic flux through $C_2$ decreases.
Net effect: decrease in outward magnetic flux through $C_2$.
Step 4: Direction of induced current.
To oppose the decrease in outward flux, the induced current in $C_2$ must produce outward magnetic field.
This corresponds to a clockwise induced current.
Final Answer: $\boxed{\text{Option (C)}}$