A magnetic field in a certain region is non-uniform and is given by

MATHEMATICS · Subjective · ISC · Mathematics · Physics · Calculus

Problem

\mathbf{B}=k x\,\hat{\mathbf{z}}

, where

k=0.020\,\text{T m}^{-1}

and

x

is the distance from the

y\!z

-plane measured along the

x

-axis. A square loop lies in the

y\!z

-plane such that its sides run from

y=0

y=0.30\,\text{m}

and from

z=0

z=0.30\,\text{m}

. The loop is located at

x=2.0\,\text{m}

. (a) Write an expression for the elemental magnetic flux

\mathrm{d}\Phi

through an elemental area

\mathrm{d}A

of the loop. (b) By integrating over the entire surface of the square, determine the total magnetic flux linked with the loop.