A quarter circular rig `(x^(2)+y^(2)=R^(2),xgt0,ygt0,z=0`) has Q charge uniformly distributed on it. Radius of the ring is `R` and its centre is at origin. Ring lie on x-y plane what can be the possible value of electrical dield at a point `(0,0,R)`?

Options

A. `-4hati-hatj+(pi)/(2)hatk`
B. `-2hati-2hatj+2hatk`
C. `-pihati-pihatj+2hatk`
D. `-2hati-2hatj+pihatk`

Answer

D

Explanation

`dE=(K(Q)/(pi//2)xxd theta)/((sqrt(2)R)^(3))[-Rcosthetahati-Rsinthetahatj+Rhatk]`

`R=(KQ)/(sqrt(2)piR^(2))int_(0)^(pi//2)[costhetahati-sinthetahatj]d theta`
`=(KQ)/(sqrt(2)piR^(2))[-hati-hatj+(pi)/(2)hatk]`
`x` and `y` component will be equal and z component will be `(pi)/(2)` times.