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

To solve this problem, let's consider the principles of electromagnetic induction and how changes in magnetic fields can induce currents in nearby coils.

1. Coils $C_1$, $C_2$, and $C_3$ are arranged with $C_2$ exactly midway between $C_1$ and $C_3$.
   • $C_1$ carries a current $I$ in the anti-clockwise direction, which will create a magnetic field pointing upwards along their common axis.
   • $C_3$ carries the same current $I$, but in the clockwise direction, creating a magnetic field pointing downwards along the axis.
   • $C_2$, being in the middle, is initially experiencing a net magnetic field from both $C_1$ and $C_3$.
2. Induced current in $C_2$ due to relative motion:
   • According to Lenz's Law, the direction of the induced current in $C_2$ will be such that it opposes the change in magnetic flux through it.
3. Analysis of options:
   • If $C_1$ moves away from $C_2$, the magnetic field at $C_2$ due to $C_1$ would decrease. Similarly, if $C_3$ moves away from $C_2$, its field contribution would also decrease.
   • If both $C_1$ and $C_3$ move towards $C_2$, the magnitudes of both fields at $C_2$ would increase.
   • Now, if $C_1$ moves towards $C_2$ while $C_3$ moves away from $C_2$, the magnetic field from $C_1$ would increase and the field from $C_3$ would decrease.
   • Considering the scenario where $C_1$ moves closer and $C_3$ moves away, the net magnetic field due to $C_1$ becomes dominant and increases in strength more significantly than the decrease from $C_3$. This induces a change that is opposed by the induced current in $C_2$.
4. Conclusion:
   • Watch closely what happens to the fields: When $C_1$ moves closer and $C_3$ moves away, the magnetic flux through $C_2$ behaving as if it is experiencing a stronger upward field due to $C_1$'s motion.
   • Therefore, by Lenz's Law, $C_2$ will have an induced current in the clockwise direction to oppose this increase, hence, establishing our answer.

Thus, the correct answer is:

$C_1$ moves towards $C_2$ and $C_3$ moves away from $C_2$