Question

a charge Q is placed at a distance d/2 above the central line of an infinite strip of width d as shown flux of the electric field through this infinite strip is​

Answer 1

Answer:(4) Q/4£°

Explanation:

We have,

Charge Q which is placed above the plane of infinite strip of finite width 'd' at a distance of d/2 from the centre line.

By Gauss's Law,

Total flux generated by the charge Q over closed surface containing it will be

$\frac{Q}{\varepsilon_o}$

But, here we need to find flux oblnly over the infinite strip of width 'd'.

So, we will find part of charge Q which covers width 'd'of strip.

So, we will calculate angle subtended by the charge over the strip.

Therefore,

In triangle ABC as seen in figure,

$tan(A) = \frac{\frac{d}{2}}{\frac{d}{2}}\\ \\=>tan(A) = 1\\ \\ =>A= \frac{\pi}{4}$

Angle to cover the strip is '2A'.

Hence, 2A=π/2 .

Now, By Gauss Law,

Flux by charge Q on

2π radial angle is Q/£° .

i.e. π/4 => Q/4£° flux.

Hence, resulting answer is

$\frac{Q}{4\varepsilon_o}$