the following diagram represents a semi circular wire of linear charge density `lambda=lambda_(0)sin theta` where `lambda_(0) `is a positive constant.The electric potential at `o` is (take `k=(1)/(4piepsilon_(0))`

Options

A. `klambda_(0)sintheta`
B. `(klambda_(0)costheta)/(2)`
C. zero
D. `klambda_(0)cos theta`

Answer

C

Explanation

`lambda=lambda_(0)sintheta`

`dQ=lambda(dl)=lambda_(0)sinthetaR(d theta)`
`rArr dV=(1)/(4piepsilon_(0))(lambda_(0)Rsintheta(d theta))/(R)`
`V=(1)/(4piepsilon_(0))lambda_(0)int_(-pi//2)^(pi//2)sintheta (d theta)`
`-(lambda_(0))/(4piepsilon_(0))(costheta)_(-pi//2)^(pi//2)=0`