Question

A parallel plate capacitor of capacitance $C$ is charged to a potential $V$. The flux of the electric field through a closed surface enclosing the space between capacitor plates is

• A. $\frac{CV}{{\epsilon }_0}$
• B. $\frac{2CV}{{\epsilon }_0}$
• C. Zero
• D. $\frac{CV}{2{\epsilon }_0}$

Answer 1

The correct option is C Zero

According to Gauss’ law, the flux of electric field through any closed surface is given by the formula, $$\varphi =\frac{q_{\text{enclosed}}}{{\epsilon }_0}$$ Where, $q_{\text{enclosed}}$ is the charge enclosed by the closed surface.

The two plates of a capacitor have equal and opposite charges. This implies that the net charge enclosed by a closed surface enclosing the capacitor plates will be zero.i.e., $q_{\text{enclosed}}=0$

As the enclosed charge is zero, so there will be no electric flux through this surface.i.e., $\varphi =0$

Hence, option (c) is the correct answer.

Key concept: Charge distribution on PPC & Gauss’ law.