Induction in Multiple Coils?

📌 CONCEPT: When a coil of wire is placed near another coil with a varying magnetic field, the changing magnetic flux induces an electromotive force (EMF) in the first coil, causing a current to flow in the galvanometer, if it is connected across the first coil.

📐 RULE / FORMULA: The magnitude of the induced current in the galvanometer is directly proportional to the rate of change of the magnetic flux linking the two coils. This can be mathematically expressed as: I ∝ dΦ/dt, where I is the induced current and Φ is the magnetic flux.

💡 WORKED EXAMPLE: Suppose a coil with 100 turns is placed near another coil with a varying magnetic field, and the first coil is moved closer to the second coil. If the rate of change of the magnetic flux increases from 0.01 to 0.1 Wb/s, how does the magnitude of the induced current in the galvanometer change? The rate of change of the magnetic flux is 10 times greater, so the magnitude of the induced current also increases by 10 times, assuming the number of turns in the first coil remains constant.

⚠️ COMMON MISTAKE: Students often forget to consider the effect of the changing magnetic flux on the induced current. They may incorrectly assume that the induced current remains constant even when the number of turns in the first coil increases, which is not true.