A flexible wire loop in the shape of a circle has a radius that grows linearly with time. There is a magnetic field perpendicular to the plane of the loop that has a magnitude inversely proportional to the distance from the center of the loop,$$B(r)$$∝$$1r$$. How does the emf E vary with time?

Question

Infinity Learn · Accepted Answer

Let radius of the loop is r at any time t and in further time dt, radius increases by dr.Then change in flux: dϕ$$=2$$$$π$$rdrB⇒$$e=d$$ϕ$$dt=2$$$$π$$$$r(drdt)kr$$⇒$$e=2$$$$π$$$$ck(constant)$$      [$$drdt=c$$,$$B=kr$$]Then change in flux: dϕ$$=2$$$$π$$rdrB

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A flexible wire loop in the shape of a circle has a radius that grows linearly with time. There is a magnetic field perpendicular to the plane of the loop that has a magnitude inversely proportional to the distance from the center of the loop,B(r)∝1r. How does the emf E vary with time?

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