A circular conducting loop has an initial radius

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

r_0 = 10\,\text{cm}

. Its radius increases uniformly with time according to

r(t)=r_0+\alpha t

, where

\alpha = 1.0\times10^{-2}\,\text{m}\,\text{s}^{-1}

. The loop is placed in a spatially uniform magnetic field that varies with time as

B(t)=B_0 e^{-k t}

, where

B_0 = 0.50\,\text{T}

and

k = 0.10\,\text{s}^{-1}

. The field vector is everywhere perpendicular to the plane of the loop and directed out of the page. (a) Derive an expression for the magnetic flux through the loop as a function of time. (b) Hence obtain an expression for the induced emf

\varepsilon(t)

at any instant. (c) Calculate the magnitude of the induced emf at

t = 2.0\,\text{s}

. (d) State whether the induced current at

t = 2.0\,\text{s}

is clockwise or counter-clockwise when viewed from the side from which the field emerges, and give a brief reason.

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