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

We need to determine when induced current in $$C_2$$ flows clockwise. Three coils on a common axis—$$C_1$$ on the left, $$C_2$$ in the middle, and $$C_3$$ on the right—carry currents of magnitude $$I$$, with $$C_1$$ carrying current anticlockwise as viewed from the left and $$C_3$$ carrying current clockwise as viewed from the left.

By the right-hand rule, the anticlockwise current in $$C_1$$ produces a magnetic field pointing to the right through $$C_2$$, while the clockwise current in $$C_3$$ produces a magnetic field pointing to the left through $$C_2$$. Since $$C_2$$ is equidistant from both coils, the net magnetic flux through $$C_2$$ is initially zero.

When $$C_1$$ moves toward $$C_2$$, the rightward flux through $$C_2$$ increases. At the same time, when $$C_3$$ moves away from $$C_2$$, the leftward flux through $$C_2$$ decreases, which is equivalent to a further increase in rightward flux. Hence the net rightward flux through $$C_2$$ increases.

By Lenz’s law, the induced current in $$C_2$$ must oppose this increase in rightward flux by producing leftward flux of its own. A clockwise current (viewed from the left) generates a leftward magnetic field inside $$C_2$$, so the induced current flows clockwise, matching Option B.

Therefore, the answer is Option B.