A single circular conducting loop of radius is located in a region where the magnetic…

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

Problem

A single circular conducting loop of radius

R

is located in a region where the magnetic field is directed normal to the plane of the loop and varies with time according to

B(t)=B_0e^{-kt}

with

B_0

and

k

positive constants. (i) Derive an expression for the induced emf as a function of time. (ii) Taking

R=0.10\,\text{m}

B_0=0.50\,\text{T}

and

k=25\,\text{s}^{-1}

, calculate the magnitude of the emf at

t=0

. (iii) After what time will the magnitude of the emf fall to

\dfrac{1}{e}

of its initial value?