Question

3. a) Consider a point charge q at the center of an imaginary box with side lengths 2a. Explicitly calculate the flux of the electric field through the box and show that it agrees with Gauss's law. b) Suppose the electric field of a point charge q is proportional to 1/r3 instead of 1/2. Does Gauss's law hold in this case? Hint: compute the electric flur through a sphere centered at the location of q. Is your answer dependent on your choice of sphere?

Answer 1

3 a)

@ = q/$\varepsilon$

This is the flux independent of any surface for a given charge

By gauss law

$\sigma$/$\varepsilon$ = E

$\sigma$ = q/24a^2

@ = EA

= q/24a^2/$\varepsilon$ x 24a^2 = q/$\varepsilon$

b)

No. Because as we can see from above example as well.

The r^2 in area and in charge density can cancel each other out. With r^3 instead, the formula will change and gauss therom cannot be reached