A massless square loop, of wire of resistance 10 Ω, supporting a mass of 1 g, hangs vertically with one of its sides in a uniform magnetic field of 10³ G directed outwards in the shaded region. A dc voltage V is applied to the loop. For what value of V will the magnetic force exactly balance the weight of the supporting mass? [Side of loop = 10 cm, g = 10 m s⁻²] Image
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Question

A massless square loop, of wire of resistance 10 Ω, supporting a mass of 1 g, hangs vertically with one of its sides in a uniform magnetic field of 10³ G directed outwards in the shaded region. A dc voltage V is applied to the loop. For what value of V will the magnetic force exactly balance the weight of the supporting mass? [Side of loop = 10 cm, g = 10 m s⁻²] Image

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G1 Physics · Accepted Answer

Balance requires ILB = mg. Since I = V/R, V = mgR/(LB). Here m = 10⁻³ kg, R = 10 Ω, L = 0.10 m and B = 10³ G = 0.10 T. Thus V = (10⁻³×10×10)/(0.10×0.10) = 10 V.