Question

A semicircular wire of radius a having λ as charge per unit length is shown in the figure. Find the electric potential at the centre of the semicircular wire. 

Options

• `lambda/epsilon_0`

• `lambda/(4piepsilon_0"R") `

• `lambda/(4epsilon_0)`

• None of these

Answer 1

`bb(lambda/(4epsilon_0))`

Explanation:

Given: Radius of semicircular wire = a

charge acting per unit length on wire = λ

potential at centre is, v = `(Sigma"q")/(4piepsilon"R")`

here `Sigma"q"=lambdapi"R"`

∴ v = `(lambdapi"R")/(4piepsilon_0"R")`

v = `lambda/(4epsilon_0)`

The electric potential at the centre of wire is `lambda/(4epsilon_0)`.