enter image description here

For this problem I am stuck on how to calculate the electric field. I know to apply Gauss' Law: $$\oint \overrightarrow{ E} \cdot \overrightarrow {dA} = \frac{q_{enclosed}}{\epsilon_0}$$ $$E(4\pi r^2) = \frac{Q + -Q}{\epsilon_0}$$ I don't know $r$, but knowing that the $Q's$ are equal magnitude can this be stated that the electric field inside is zero?

  • $\begingroup$ Is the answer E? $\endgroup$ Sep 21 '20 at 4:22
  • $\begingroup$ That's what I am trying to verify, but I don't know if my approach is valid. $\endgroup$
    – E__
    Sep 21 '20 at 4:25
  • 1
    $\begingroup$ I am writing an answer wait $\endgroup$ Sep 21 '20 at 4:27

Consider a point $D$ on in the meat of the conductor as shown.

enter image description here

We know that field inside the meat of a conductor is zero. So, electric field at $D$ is zero for all positions of $D$. Hence, the distribution on the outer surface of the sphere must be uniform so that it behaves like a shell. Also, the net charge on the surface is equal to the net charge inside a conductor. Hence, you may replace the conductor by an uncharged sphere to analyze Electric field and Potential outside the conductor.

So, your answer is $0$.


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