# If a unit positive charge is placed inside a sphere of radius r, then the electric flux through the sphere will be:

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If a unit positive charge is placed inside a sphere of radius r, then the electric flux through the sphere will be:
1. ϵor
2. $\frac{ϵ_o}{r}$
3. $ϵ_o^{-1}$
4. ϵo

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Correct Answer - Option 3 : $ϵ_o^{-1}$

CONCEPT:

Gauss's law:

• According to Gauss law, the total electric flux linked with a closed surface called Gaussian surface is $\frac{1}{ϵ_o}$ the charge enclosed by the closed surface.

$⇒ ϕ=\frac{Q}{ϵ_o}$

Where ϕ = electric flux linked with a closed surface, Q = total charge enclosed in the surface, and ϵo = permittivity

Important points:

1. Gauss’s law is true for any closed surface, no matter what its shape or size.
2. The charges may be located anywhere inside the surface.

EXPLANATION:

Given Q = 1, and r = radius of the sphere

​By the Gauss law, if the total charge enclosed in a closed surface is Q, then the total electric flux associated with it will be given as,

$⇒ ϕ=\frac{Q}{ϵ_o}$     -----(1)

By equation 1 the total flux linked with the sphere is given as,

$⇒ ϕ=\frac{Q}{ϵ_o}$

$⇒ ϕ=\frac{1}{ϵ_o}$

$⇒ ϕ = ϵ_o^{-1}$

• Hence, option 3 is correct.