Question

A point charge Q is placed at the center of a conducting spherical shell (inner radius a, outer radius b). What is the electric field at a point a distance r from Q? Consider the cases r < a, a < r < b, and r > b.

Answer 1

a)
`E=(Q)/(\varepsilon _o* 4\pi r^2)\ N/C`

b)E=0

c)
`E=(Q)/(\varepsilon _o* 4\pi r^2)\ N/C`

Step-by-step explanation:

Given that

A point charge Q is placed at the center of a conducting spherical shell .Due to this - Q charge will induce on the inner sphere surface and +Q will induce on the outer sphere surface .

a) r < a

At a radius r ,from gauss theorem

`E.ds=(q_i)/(\varepsilon _o)`

`E* 4\pi r^2=(Q)/(\varepsilon _o)`

`E=(Q)/(\varepsilon _o* 4\pi r^2)\ N/C`

b) a < r < b

`E.ds=(q_i)/(\varepsilon _o)`

The total induce in this surface = - Q+ Q =0

`E.ds=(0)/(\varepsilon _o)`

E = 0

c) r > b

`E.ds=(q_i)/(\varepsilon _o)`

`E* 4\pi r^2=(Q)/(\varepsilon _o)`

`E=(Q)/(\varepsilon _o* 4\pi r^2)\ N/C`