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) + vt, where r0 - 0.250 m and v = 0.0290 m/s. The loop has a constant resistance of R = 19.3 Ohm and is placed in a uniform magnetic field of magnitude B0 = 1.71 T, perpendicular to the plane of the loop, as shown In the figure. Calculate the direction and the magnitude of the induced current. l, at t = 4.91 s. (Use positive numbers for a clockwise current and negative numbers for a counterclockwise current.)

Explanation / Answer

magnetic flux () = 1.71*(.25+ 0.0290t)2

E = -d/dt , t= 4.91= 0.122 V

current will be induced in clockwise direction = 0.122/19.3= +6.33 mA

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