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 = 0.230 m and v = 0.0210 m/s. The loop has a constant resistance of R = 13.1 Ohm and is placed in a uniform magnetic field of magnitude B0 = 1.31 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 = 3.77 s. (Use positive numbers for a clockwise current and negative numbers for a counterclockwise current.)

Explanation / Answer

According to lenz law the current induces in such a way to oppose the change in flux.since flux dirctly depends on area and area is increasing so flux is also increasing with time hence current will be in clockwise such that magnetic field due to induced current opposes the change of flux. FLux = BAcos(0) Flux = f = BA now, EMF = df/dt = Bp(dr^2/dt) = pB d ( r0 + vt)/dt = pBv Now Current = I = EMF/R = pBv/R = p x 1.31 x 0.021 /13.1 = 0.006597 A or 6.59 mA,current is clockwise

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