A square loop of side L and mass m is standing on a table on one of its sides. T

Question

A square loop of side L and mass m is standing on a table on one of its sides. The loop has a total resistance of R. There is a uniform magnetic field B such that initially the field is going through the loop perpendicularly. The loop is given a very small displacement and allowed to fall without sliding. At some time t, the angular position of the loop is THETA and the angular speed is OMEGA.

a.) What is the flux through the coil at time t? [1]

b.) What is the induced e.m.f and current in the loop at time t? Indicate both magnitude and direction. A drawing may help. [2]

c.) Suppose the moment of inertia of the loop about the pivot axis is I, write down a differential equation for THETA by energy consideration. [2]

d.) Explain why this loop can fall much slower than it does in a field-free region. [1]

Explanation / Answer

(a) B*cos(theta)*L^2

(b) omega*L^2*B V , omega*L^2*B/R A at the topmost point current is out of the plane

(c) m*g*L*(1-cos(theta))= I*omega^2

(d) magnetic force acting upward

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