Question

Consider a Gaussian surface that encloses no net charge. (a) Does Gauss's Law require that E = 0 at all points on the surface? (b) Is the converse true, that is, (b) If E = 0 at all points on the surface does Gauss's Law require that there be no net charge inside the surface? 6.

Answer 1

a) No, Gauss's law only requires that integration of E.ds all over the surface is zero. This does not necessarily require the field to be zero at all points.

b) Yes, it's true, because according to Gauss's law, flux,

$\phi = \frac{q_{enclosed}}{\epsilon_o}$

Now,

$\phi = \int E.ds$

So, if E = 0 at all points then

$\phi = 0$

which means,

$0 = \frac{q_{enclosed}}{\epsilon_o}$

or, q_enclosed = 0

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