Case Study
Passage with linked questions
Case Set 1
Case AnalysisPassage
A physics teacher demonstrates electromagnetic induction to her class using a bar magnet and a coil connected to a galvanometer. She pushes the north pole of a strong bar magnet toward the coil at moderate speed and the galvanometer deflects to the right. She then holds the magnet stationary inside the coil — the deflection drops to zero. Next, she pulls the magnet out rapidly and the galvanometer deflects sharply to the left. Finally, she replaces the bar magnet with the south pole facing the coil and repeats the push — the galvanometer deflects to the left. The students are asked to analyse each observation and relate it to Faraday's law and Lenz's law. The teacher emphasises that the magnitude of deflection is related to the rate of change of magnetic flux and not merely the strength of the magnet.
Question 1: Why does the galvanometer show no deflection when the bar magnet is held stationary inside the coil?
- When the magnet is stationary, the magnetic field through the coil is constant, so the magnetic flux ΦB does not change with time.
- Since dΦB/dt = 0, Faraday's law gives ε = −N(dΦB/dt) = 0, meaning no emf is induced and hence no current flows through the galvanometer.
Question 2: Why is the galvanometer deflection sharper when the magnet is pulled out rapidly compared to when it is moved slowly?
- The induced emf is given by ε = −N(dΦB/dt); when the magnet is pulled out rapidly, the rate of change of magnetic flux dΦB/dt is larger in magnitude.
- A larger dΦB/dt produces a larger induced emf and hence a larger induced current, causing a greater deflection of the galvanometer pointer.
Question 3: Using Lenz's law, explain why the galvanometer deflects in opposite directions when (i) the north pole is pushed in and (ii) the north pole is pulled out.
- When the north pole is pushed toward the coil, the magnetic flux through the coil increases. By Lenz's law, the induced current must oppose this increase and flows in a direction that makes the near face of the coil a north pole — repelling the approaching magnet; this corresponds to deflection to the right.
- When the north pole is pulled away, the flux through the coil decreases. The induced current now flows in the opposite direction, making the near face a south pole — attracting the receding magnet and opposing the decrease in flux; this corresponds to deflection to the left.
- In both cases the induced current opposes the change in flux (not the flux itself), consistent with Lenz's law: ε = −N(dΦB/dt), where the negative sign encodes this opposition. This also ensures energy conservation — work must be done against the opposing force in each case.