Two long coaxial solenoids share the same axis. The primary solenoid has 250 turns and the secondary has 180 turns. Their mutual inductance is 0.09 H. If the current in the primary decreases linearly from 5 A to 0 A in 0.004 s, (i) calculate the magnitude of the emf induced in the secondary coil, (ii) state the direction of the induced current in the secondary relative to the direction of the primary current just before it started to decay.

Step-by-step solution

1. Find the rate of change of primary current: $di/dt=(0-5)/0.004=-1250{\text{ A s}}^{-1}$.
2. Use the mutual inductance emf relation: ${\epsilon }_{\text{secondary}}=-M,\frac{di}{dt}$.
3. Compute the magnitude: $|\epsilon |=0.09\times 1250=112.5\text{ V}$.
4. Apply Lenz’s law: a decreasing primary current tries to reduce further, so the induced magnetic field in the secondary must oppose the decrease and therefore be in the same sense as the original primary field. Consequently the induced current in the secondary flows in the same direction as the original primary current.

Concept tested: Mutual inductance and Lenz’s law

Published 18 September 2026 · How this solution was prepared and checked