A cone made of insulating material has a total charge Q spread uniformly over its sloping surface. Calculate the work done in bringing a small test charge q from infinity to the apex of the cone. The cone has a slope length L.

Answer

D

Explanation

`W_(infty) to A=qVA, `Calculation of `V_A`
Charge on ring element `dq=0/(pi RL) (2 pi l sin theta dl)`
`dV=(Kdq)/l=k/l (2Q l sin theta dl)/(RL)`
`V_A= int dV=(2kQ sin theta)/(RL) int dl =(2kQ)/(RL) R/L L =(2KQ)/L`
`(2KQq)/L= (2 times 9 times 10^9 times 3 times 10^-3 times 5 times 10^-6)/R times 3/5=81J =3^4 J`. On comparing `3^x=3^4 therefore x=4`