A square loop of side length d has mass m, inductance L and zero resistance. It

Question

A square loop of side length d has mass m, inductance L and zero resistance. It is placed in the ry plane, centered at the origin and with its sides parallel to the r and y axes. The magnetic field in this region of space can be described by Boê, if 0 The loop is given an initial velocity v vo. (a) Which direction does the current start to initially flow in the loop? (b) Which direction in the initial force on the loop? (c) By relating the force to the current which in turn is related to the change in flux, derive a differential equation for v. (d) Solve this differential equation to determine the motion of the loop at later times. (e) What is the peak current generated in the loop?

Explanation / Answer

a) Initially the current start to flow in an anti-clockwise direction .

b) The direction of an initial force is towards left .

c) The differential equation for loop velocity is,

dv/dt + [(m * vo * Bo)/(Ld)] * t = 0

d) By solving above differential equation, we get

=> v = vo * (e)-Ld/mBo

e) Peak current generated = (vo * m * Bo) / L

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