Question

As shown, three coils are given. The first and the last coils carry equal currents. Choose the correct option for the second inductor so that it has clockwise current.

• A. Move \(L_1\) towards \(L_2\) and \(L_3\) away from \(L_2\).
• B. Move \(L_1\) away from \(L_2\) and \(L_3\) away from \(L_2\).
• C. Move \(L_1\) towards \(L_2\) and \(L_3\) towards \(L_2\).
• D. Move \(L_1\) away from \(L_2\) and \(L_3\) towards \(L_2\).

Hint:

To solve electromagnetic induction problems:
First determine whether magnetic flux is increasing or decreasing
Then apply Lenz’s law to decide the direction of induced current
Treat effects of multiple sources separately and then combine

Answer 1

The Correct Option is A

Concept: 
The direction of induced current in a coil is determined by Lenz’s law. According to Lenz’s law:  The induced current flows in such a direction that it opposes the change in magnetic flux producing it.  Key ideas used: 
Approaching coils increase magnetic flux 
Receding coils decrease magnetic flux 
The induced current always opposes the {change} in flux, not the flux itself 
Step 1: Effect of coil \(L_1\) on coil \(L_2\). The current in \(L_1\) is anticlockwise. If \(L_1\) is moved towards \(L_2\), the magnetic flux through \(L_2\) due to \(L_1\) increases. To oppose this increase, the induced current in \(L_2\) must produce a magnetic field in the opposite direction, which corresponds to a clockwise current. 
Step 2: Effect of coil \(L_3\) on coil \(L_2\). The current in \(L_3\) is clockwise. If \(L_3\) is moved away from \(L_2\), the magnetic flux through \(L_2\) due to \(L_3\) decreases. To oppose the decrease in flux, the induced current in \(L_2\) must try to maintain the original flux direction, again requiring a clockwise current. 
Step 3: Combine both effects. Both actions: 
Moving \(L_1\) towards \(L_2\) 
Moving \(L_3\) away from \(L_2\) produce induced currents in \(L_2\) in the same (clockwise) direction. Hence, this combination ensures that the current in the second coil is clockwise. \[ \boxed{\text{Correct option is (1)}} \]