Faraday's law: Induced EMF is the negative rate of change of magnetic flux

Steps:

• Magnetic flux through coil φ = BA cosθ, where θ is angle between normal to plane and B; initially θ = 0°, flux maximum.
• Coil rotates at steady rate, so θ = ωt, increasing linearly from 0° to 180°.
• Induced EMF ε = -dφ/dt = BAω sinθ.
• As θ goes from 0° to 180°, sinθ goes from 0 to 1 (at 90°) back to 0, producing a sinusoidal variation starting and ending at zero.

Why A is correct:

• Matches ε ∝ sinθ, showing smooth increase to maximum at 90° then decrease to zero at 180°, per Faraday's law.

Why the others are wrong:

• B: Shows constant EMF, ignoring flux variation with θ.
• C: Depicts linear change, assuming uniform flux decrease rather than cosθ dependence.
• D: Illustrates full sine wave oscillation, incorrect for 180° rotation without reversal.

Final answer: A