Question

A point charge q1 = -7.7 μC is located at the center of a thick conducting spherical shell of inner radius a = 2.2 cm and outer radius b = 4.5 cm, The conducting spherical shell has a net charge of q2 = 2.6 μC. 1)What is Ex(P), the value of the x-component of the electric field at point P, located a distance 8.8 cm along the x-axis from q1?

Answer 1

`E_x = -5.93 * 10^6`

Explanation:

Parameters given:

Point charge at the center of the sphere,
`q_1` :
`-7.7 * 10^(-6)`μC

Charge of the sphere,
`q_2` :
`2.6 * 10^(-6)`μC

Distance between
`q_1` and the point of consideration =
`8.8 * 10^(-2) m`

Distance between
`q_2` and the point of consideration =
`8.8 * 10^(-2) m`

Electric field is given as

`E_x = (kq)/(r^2)`

where

k = Coulombs constant;

q = electric charge;

r = distance between charge and point of consideration.

The net electric field at that point is the sum of the electric field due to
`q_1` and
`q_2`, i.e.:

`E_x = (kq_1)/(r^2) + (kq_2)/(r^2)`

Since k is the same and the distance, r is also the same, then:

`E_x =(k)/(r^2) ( q_1 + q_2)`

=>
`E_x =(9 * 10^9)/((8.8 * 10^(-2))^2) [ (-7.7 * 10^(-6)) + (2.6 * 10^(-6))]`

=>
`E_x = 1.162 * 10^(12) * -5.1 * 10^(-6)\\\\\\E_x = -5.93 * 10^6`

The electric field along the x axis,
`E_x = -5.93 * 10^6`