Question 5

**Setting up the motion** While the loop is partially inside the field (0 < y < L for the leading edge), the flux changes, giving - EMF = B₀Lv, current I = B₀Lv/R - Retarding force F = B₀IL = B₀²L²v/R = KMv So M dv/dt = −KMv ⟹ v = v₀e^(−Kt), and the distance covered is x(t) = (v₀/K)(1 − e^(−Kt)), approaching v₀/K asymptotically. **(A)** v₀ = 1.5KL ⟹ limiting distance v₀/K = 1.5L > L. The loop does enter completely (leading edge reaches y = L at finite time). **False.** **(B)** Once fully inside, flux through the loop is constant ⟹ no induced current ⟹ no magnetic force. Net force zero. **True.** **(C)** v₀ = KL/10 ⟹ limiting distance = L/10 < L, so the loop never enters fully, but the velocity v = v₀e^(−Kt) decays exponentially and never becomes zero at any finite time. It does not "come to rest" at t = (1/K)ln(5/2). **False.** **(D)** v₀ = 3KL: set x = L ⟹ 3L(1 − e^(−Kt)) = L ⟹ e^(−Kt) = 2/3 ⟹ t = (1/K)ln(3/2). **True.**

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