A conducting square loop of side L, mass M and resistance R enters a region y ≥ 0 containing uniform magnetic field B = B₀ k̂ with initial velocity v₀ ĵ. Define K = B₀²L²/(RM). Ignoring self-inductance and gravity, which statements are correct? Image
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Question

A conducting square loop of side L, mass M and resistance R enters a region y ≥ 0 containing uniform magnetic field B = B₀ k̂ with initial velocity v₀ ĵ. Define K = B₀²L²/(RM). Ignoring self-inductance and gravity, which statements are correct? Image

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G1 Physics · Accepted Answer

While the loop is partially entering, magnetic drag is F = −(B₀²L²/R)v = −MKv. Thus dv/dt = −Kv and, using dv/dt = v dv/dx, dv/dx = −K ⇒ v = v₀ − Kx. The loop fully enters when x = L. A: for v₀ = 1.5KL, v(L) = 0.5KL > 0, so it does not stop before entering fully. False. B: once the loop is completely inside a uniform field, the flux no longer changes; induced current and magnetic drag become zero. True. C: for v₀ = KL/10, stopping distance v₀/K = L/10. The speed approaches zero asymptotically;…