Motion of loop inductor in magnetic field A square loop of side length d has mas

Question

Motion of loop inductor in magnetic field A square loop of side length d has mass m, inductance L and zero resistance. It is placed in the xy plane, centered at the origin and with its sides parallel to the x and y axes. The magnetic field in this region of space can be described by B = {B_0 z^, if x lessthanorequalto 0 0, if x > 0 The loop is given an initial velocity v = v_0x^. In which direction does the current start to initially flow in the loop? In which direction is the initial force on the loop? By relating the force to the current which in turn is related to the change in flux, derive a differential equation for the loop velocity. Solve this differential equation to determine the motion of the loop at later times. What is the peak current generated in the loop?

Explanation / Answer

a) Direction current start initial flow = anticlockwise direction .

b) Direction initial force = towards left .

c) differential equation for loop velocity -

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

d) Solving above differential equation -

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

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

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