A particle carrying charge +q is placed at the center of a thick-walled conducting shell that has inner radius R and outer radius 2R and carries charge −2q. A thin-walled conducting shell of radius 5R carries charge +2q and is concentric with the thick-walled shell. Define V = 0 at infinity. Calculate all distances from the particle at which the electrostatic potential is zero.

10R/11 and 5R/2

Explanation:

The radius of the conducting shell = R,

Electrostatic potential inside the shell (r<R) = kq/R

Electrostatic potential outside the shell (r>R) = kq/r

If x is the point of zero potential

Electrostatic potential for inner shell,

Electrostatic potential for outer shell,

Electrostatic potential for the thin walled shell,

The values of X=r that satisfy the above equation are 10R/11 and 5R/2

mistakes are ok

it is a negative acceleration