An elastic circular conducting loop expands at a constant rate over time such th

Question

An elastic circular conducting loop expands at a constant rate over time such that its radius is given by r(t) = r0 + vt, where r0 = 0.110 m and v = 0.0290 m/s. The loop has a constant resistance of R = 11.9 ? and is placed in a uniform magnetic field of magnitude B0 = 1.65 T, perpendicular to the plane of the loop, as shown in the figure. Calculate the direction and the magnitude of the induced current, i, at t = 5.55 s. (Use positive numbers for a clockwise current and negative numbers for a counterclockwise current.)

An elastic circular conducting loop expands at a constant rate over time such that its radius is given by r(t) = r0 + vt, where r0 = 0.110 m and v = 0.0290 m/s. The loop has a constant resistance of R = 11.9 ? and is placed in a uniform magnetic field of magnitude B0 = 1.65 T, perpendicular to the plane of the loop, as shown in the figure. Calculate the direction and the magnitude of the induced current, i, at t = 5.55 s. (Use positive numbers for a clockwise current and negative numbers for a counterclockwise current.)

Explanation / Answer

flux=B.A

A=pie*r^2

sp V=dflux/dr

=B*d(ro+vt)^2/dt*pie

=2Bv(ro+vt)*pie

=0.08141 V

so the current=v/R

=6.842*10^-3 A (counterclockwise)

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