A capacitor of capacitance C is charged to a potential V . The flux...

A capacitor of capacitance

C

is charged to a potential

V

. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is: A capacitor of capacitance C is charged to a potential V . The flux of the electric field through a closed surface

A capacitor of capacitance C is charged to a potential V . The flux of the electric field through a closed surface

Options

A $\dfrac{CV}{{ε}_{0}}$
BZero
C $\dfrac{2CV}{{ε}_{0}}$
D $\dfrac{CV}{2{ε}_{0}}$

Correct answer

A. $\dfrac{CV}{{ε}_{0}}$

Step-by-step solution

A capacitor of capacitance C is charged to a potential V . The flux of the electric field through a closed surface
The charge enclosed is given by ${q}_{inc} = CV$

Gauss' law states that the flux through any closed surface is equal to the charge enclosed by the surface.

Using Gauss' law the flux is, $ϕ = \dfrac{{q}_{\text{inc}}}{{ε}_{0}} = \left(\dfrac{CV}{{ε}_{0}}\right)$

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