Question

an infinitely large thin thin sheet has a uniform surface charge density + Sigma obtain the expression for the amount of work done in bringing a point charge Q from infinity to a point distance R in front of a charged plane sheet​

Answer 1

The work done is zero

Explanation:

The sheet is of infinite dimension , having uniform charge density .

Thus electric field  E = σ/2ε₀ , which is constant .

The force exerted on the charge Q = Q E , which is the same at all points .

Therefore to move the charge in the field of sheet no force is required . Thus no work will be done .

It is called equipotential surface also .

Answer 2

Given that,

Charge density of sheet = σ

Point charge = Q

We know that,

The electric field is

$E=\dfrac{\sigma}{2\epsilon_{0}}$

Potential at a distance from the plate is

$V=Ed$

Put the value of E

$V=\dfrac{\sigma}{2\epsilon_{0}}d$

We need to calculate the amount of work done in bringing a point charge Q from infinity to a point

Using formula of work done

$W=QV$

$W=Q\dfrac{\sigma}{2\epsilon_{0}}d$

Hence, The amount of work done is $Q\dfrac{\sigma}{2\epsilon_{0}}d$