A coil with turns and fixed cross-sectional area is oriented so that its area vector…

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

Problem

A coil with

N=200

turns and fixed cross-sectional area

4.0\times10^{-4}\,\text{m}^2

is oriented so that its area vector is parallel to an external magnetic field that varies with time according to

B(t)=0.50e^{-3.0t}\,\text{T}

, where

t

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

\mathcal{E}(t)

in the coil as a function of time. (b) Evaluate

\mathcal{E}

t=0.20\,\text{s}

and include the appropriate sign.