Question

A 2 nC point charge is embedded at the center of a nonconducting sphere of radius = 4.8 cm which has a charge of 1 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point that is 2.4 cm from the center of the sphere? Write your answer in terms of kN/C.

Answer 1

Answer:
`3.32* 10^4\ kN/C`

Step-by-step explanation:

Given

Charge at the center of the sphere is
`q=2\ nC`

Charge distributed over the entire sphere
`Q=1\ nC`

Radius of sphere
`r=4.8\ cm`

Using Guass law

`\Rightarrow \oint \vec{E}\cdot \vec{dA}=(q_(enc))/(\epsilon_o)\\\\\Rightarrow E\cdot 4\pi r^2=(1)/(\epsilon)(q+(Q)/(4\pi R^2)* 4\pi r^2)\\\\\Rightarrow E\cdot 4\pi r^2=(1)/(\epsilon)(q+Q(r^2)/(R^2))\\\\\Rightarrow E\cdot (2.4* 10^(-2))^2=9* 10^9(2+1\cdot (1)/(4))* 10^(-9)\\\\\Rightarrow E=3.32* 10^4\ kN/C`