Question

Charge Q is uniformly distributed throughout an insulating spere of radius R .The magnitude of the electric field at R/2 from center is?

Answer 1

According to the Gauss's law, $\Phi_E = \dfrac{Q}{\varepsilon_0}$ - the net electric flux through any hypothetical closed surface is equal to $\dfrac{1}{\varepsilon _0}$ times the net electric charge within that closed surface. If we chose the closed surface as marked with the thin line inside the insulating spere on the figure:

then the net electric charge within that surface is zero. Thus, the electric flux (and hence magnitude of the electric field) at R/2 from center is also 0.

Answer. E = 0 V/m.