PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# 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. - PUC Karnataka Science Class 12 - Physics

ConceptUniformly Charged Infinite Plane Sheet and Uniformly Charged Thin Spherical Shell (Field Inside and Outside)

#### 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)

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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).
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