A conducting square loop initially lies in the XZ plane with its lower edge hinged along the X-axis. Only in the region y ≥ 0 there is a time-dependent magnetic field B(t) = B₀ cos(ωt) k̂. At t = 0 the loop starts rotating with angular speed ω about the X-axis in the clockwise direction as viewed from +X. Ignoring self-inductance and gravity, choose the correct induced e. m. f. V versus time graph. Image
Options

Question

A conducting square loop initially lies in the XZ plane with its lower edge hinged along the X-axis. Only in the region y ≥ 0 there is a time-dependent magnetic field B(t) = B₀ cos(ωt) k̂. At t = 0 the loop starts rotating with angular speed ω about the X-axis in the clockwise direction as viewed from +X. Ignoring self-inductance and gravity, choose the correct induced e. m. f. V versus time graph. Image

Options

G1 Physics · Accepted Answer

For 0 < ωt < π, the loop lies in the magnetic-field region. If A is the loop area, Φ = B₀A cos(ωt) sin(ωt) = (B₀A/2) sin(2ωt). Hence V = −dΦ/dt = −B₀Aω cos(2ωt). For π < ωt < 2π the loop is in y < 0, where the magnetic field is zero, so V = 0. The pattern repeats in the next cycle. This piecewise behavior corresponds to Image 1, i.e. option A.