Question

Consider three metal spherical shells A, B and C, each of radius R. Each shell is having a concentric metal ball of radius R/10. The spherical shells A, B and C are given charges +6q, −4q, and 14q respectively. Their inner metal balls are also given charges −2q, +8q and −10q respectively. Compare the magnitude of the electric fields due to shells A, B and C at a distance 3R from their centres.

Answer 1

Three conducting spherical shells A, B, and C, each of radius R, have inner concentric metal balls of radius R/10.

Given charges are:

Shell A = +6q,

Inner ball A = −2q,

Shell B = −4q,

Inner ball B = +8q,

Shell C = +14q,

Inner Ball C = −10q

Distance where the field is to be calculated = 3R

When computing the field outside a conducting spherical shell, the total charge appears to be concentrated at the center. The inner ball creates charges on the shell’s inner surface, but the overall charge on the outside shell doesn't change. Therefore, the electric field at 3R is determined by the net charge on each shell.

Shell A:

Net charge on the shell itself = +6q

Shell B:

Net charge on the shell itself = −4q

Shell C:

Net charge on the shell itself = +14q

Now the electric fields at a distance 3R are given by

`(k6q)/((3R)^2) : (k4q)/((3R)^2) : (k14q)/((3R)^2)`

6 : 4 : 14

i.e., 3 : 2 : 7