Correct Option: (B) resistance of the coil
Step 1 (Formula / Governing Law & Given Data): [0.5 Mark]
According to Faraday’s Law of Electromagnetic Induction, the magnitude of the induced electromotive force ($e$) in a coil is given by the rate of change of magnetic flux ($\Phi_B$) linked with the coil:
$$e = -N \frac{d\Phi_B}{dt}$$Where:
- $N$ = Number of turns in the coil.
- $\Phi_B = B \cdot A \cdot \cos(\theta)$ (Magnetic flux).
- $A$ = Area of the coil.
- $\frac{d\Phi_B}{dt}$ = Rate of change of flux, which depends on the speed of the magnet.
Step 2 (Step-by-Step Mathematical Working): [0.25 Mark]
Analyzing the dependence of induced emf ($e$):
- $e \propto N$: The emf depends on the number of turns.
- $e \propto \frac{d\Phi_B}{dt}$: Since $\Phi_B$ changes as the magnet moves, the speed of the magnet directly affects the rate of change of flux.
- $e \propto A$: The flux $\Phi_B$ is directly proportional to the area $A$ of the coil.
- The resistance ($R$) of the coil determines the induced current ($I = \frac{e}{R}$), but it does not affect the magnitude of the induced emf itself.
Step 3 (Final Concluded Answer): [0.25 Mark]
Since the induced emf is defined solely by the change in magnetic flux and the geometry of the coil ($N$ and $A$), the resistance of the coil has no effect on the magnitude of the induced emf. Therefore, the correct option is (B).
💡 EL10 Concept Insight: Think of the induced emf as the "electrical pressure" created by the moving magnet; the resistance is just how hard it is for current to flow through the wire, but it doesn't change the amount of pressure the magnet creates in the first place.