A single-turn rectangular conducting coil of resistance is placed so that a uniform…

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A single-turn rectangular conducting coil of resistance

2.0\,\Omega

is placed so that a uniform magnetic field of

0.40\,\text{T}

is normal to its plane. The coil is driven mechanically so that its area varies with time according to

A(t)=0.05\sin(100\pi t)\,\text{m}^2,

where

t

is in seconds. (a) Obtain an expression for the induced emf

\mathcal E(t)

as a function of time. (b) Write the expression for the induced current

i(t)

in the coil. (c) Calculate the r.m.s. value of the induced emf over one complete cycle of the motion.