#### Question

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

#### Solution

As we know, electric field due to a uniformly charged infinitely large plane thin sheet with surface charge density σ is `E = σ/(2ε_o)`. Therefore, the amount of work done (against the electric field E) in bringing a point charge q from infinity to a point, distant r, in front of the charged plane sheet is

`W =∫_0^r F. dr`

where, F is the force experience by the charge q due to electric field E.

or W= F.r

Now,

F = Eq

⇒ W=Eqr

Here, `E= σ/(2ε_o)`

Therefore, `W= (σqr)/(2ε_o)`

Is there an error in this question or solution?

Solution An infinitely large thin plane sheet has a uniform surface charge density +σ. Obtain the expression for the amount of work done in bringing a point charge q from infinity to a point, distant r, in front of the charged plane sheet. Concept: Uniformly Charged Infinite Plane Sheet and Uniformly Charged Thin Spherical Shell (Field Inside and Outside).