EMF in Moving Loop — Non-Uniform FieldHardQuestion 20236
Question
A square loop (side a) moves with velocity v in a field B = B₀x (increasing in x direction). If the loop moves in the +x direction, the induced EMF is:
- A0
- BB₀va²Correct
- CB₀va
- DB₀v²a
Correct answer
B₀va²
Explanation
EMF = −dΦ/dt. Flux Φ = ∫B dA = ∫B₀x · a dx over the loop's extent. As the loop moves, the rate of change involves both the field variation and the velocity. For a square loop of side a at position x: Φ = B₀ × (mean x in loop) × a² = B₀(x + a/2)a². dΦ/dt = B₀(dx/dt)a² = B₀va². So |EMF| = B₀va².