Question

Assignment Vocou Colculate E field eserywhore. Concent Spheres

Help me to solve it. (Physics II)

Answer 1

The problem can be solved by using Gauss's Law,

$\int _S \vec{E}.d\vec{a} = \frac{q_{en}}{\epsilon _0}$

where $q_{en}$ = the enclosed charge.

Since a sphere is symmetric,

$\vec{E}.d\vec{a} = Edr$

And, thus,

$\int _S Eda= \frac{q_{en}}{\epsilon _0}$

$E\int _Sda= \frac{q_{en}}{\epsilon _0}$

$E\left ( 4 \pi r^2 \right )= \frac{q_{en}}{\epsilon _0}$

$E= \frac{1}{4 \pi \epsilon _0}\frac{q_{en}}{r^2}$

where r is the distance of the point of interest from center.

For position a:

$E_a= \frac{1}{4 \pi \epsilon _0}\frac{q}{r^2}$

For position b:

$E_b= \frac{1}{4 \pi \epsilon _0}\frac{-2q}{r^2}$

For position c:

$E_c= \frac{1}{4 \pi \epsilon _0}\frac{3q}{r^2}$