Question

An infinitely large thin plane sheet has a uniform surface charge density + sigma.obtain the expression for the amount of work done in bringing a point charge q form from infinity to a point, distance r in front of the charged plane sheet

Answer 1

Explanation:

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Answer 2

Work done in bringing a point charge q form from infinity to a point, distance r in front of the charged plane sheet is $W=\dfrac{q\times\sigma\times r}{\epsilon_o}$.

Given :

Surface  charge density , $\sigma$ .

We know, Electric Field due to an infinitely large thin plane sheet has a uniform surface charge density $\sigma$ is :

$E=\dfrac{\sigma}{\epsilon_o}$

Now , Work done is , $W = F.r = Frcos\theta= F\times r$  ......equation 1  ( because theta is 0 )

So, Force experienced by charge q  is , F = qE .

$F=\dfrac{ q\times \sigma}{\epsilon_o}$

Putting value of F in equation 1 .

We get :

$W=\dfrac{q\times\sigma\times r}{\epsilon_o}$

Hence , this is the required solution .

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