Find the electric field potentail and strength at the centre of a hemisphere fo raidus `R` ahcged uniformly with the the surface density `sigma`.

Options

A. `(sigmaR)/(epsilon_(0)`
B. `(2sigmaR)/(epsilon_(0))`
C. `(sigmaR)/(2epsilon_(0))`
D. `(sigmaR)/(3epsilon_(0))`

Answer

A

Explanation

The area of shaded element is `dA=2pirRd theta`
`=2piR^(2)sintheta d theta rArr dV=(1)/(4piepsilon_(0))(dq)/(R)`
`=(1)/(4piepsilon_(0))(sigma2piR^(2)sinthetad theta)/(R)=(sigma R)/(2epsilon_(0))sinthetad theta`
`V=(sigmaR)/(2epsilon_(0))int_(0)^(pi//2)sintheta d theta =(sigmaR)/(2epsilon_(0))`