A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the capacitor is
Given: a capacitor of capacitance C charged to a potential V
Gauss’s law:
Electric flux ϕ) through a closed surface S is given by
Where,
Q is the charge enclosed by S
εo is the permittivity of the free space
According to the gauss law
Electric flux,
Where
Q is the total charge enclosed in the gaussian surface
εo is the absolute permittivity of the vacuum
Since, the two plates of capacitor contains equal and opposite charges
∴ Total charge enclosed by the surface ⇒ Q-Q=0
Putting the values of total charge in gauss law, we get
∴ the electric flux through the closed surface enclosing the capacitor=0.