An infinite plane slab of thickness extends from to along the -axis and is infinite…

PHYSICS · Multi-part · CBSE · Physics · Moving Charges and Magnetism · Moving Charges and Magnetism

Problem

An infinite plane slab of thickness

2d

extends from

y=-d

y=+d

along the

y

-axis and is infinite in the

x

- and

z

-directions. Throughout the region

-d<y<0

it carries a uniform current density

\mathbf{J}=J\hat{z}

, while in the region

0<y<d

it carries an equal current density in the opposite direction,

\mathbf{J}=-J\hat{z}

. (i) Derive an expression for the magnetic field

\mathbf{B}(y)

for all points inside the slab

(|y|<d)

. (ii) Obtain

\mathbf{B}(y)

for regions outside the slab

(|y|>d)

. (iii) Sketch the variation of the magnitude of

B

with

y

from

y=-2d

y=+2d

and indicate clearly the direction of the field in each region.