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 = 0.250 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, i, at t = 4.91 s. (Use positive numbers for a clockwise current and negative numbers for a counterclockwise current.)

Explanation / Answer

1. Calculate the magnetic flux via the coil
(t)=B*A(t)

A(t)=*r(t)2=(r0+vt)2

2. Find the EMF

(t)=d/dt=2(r0+vt)*v

3. Find the current

I(t)=/R=2(r0+vt)*v/R

I(4.91)=2(0.25+0.029*4.91)*0.029/19.3=1.34*10-3 A

Current direction will be according to Lrntz law: clockwise

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