Two similar cubes A and B contains a charge q and 2q respectively, then the ratio of the flux associated with the cube A to the cube B will be:

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Two similar cubes A and B contains a charge q and 2q respectively, then the ratio of the flux associated with the cube A to the cube B will be:
1. 1 : 2
2. 2 : 1
3. 1 : 1
4. None of these

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Correct Answer - Option 1 : 1 : 2

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.

$\Rightarrow ϕ=\frac{Q}{ϵ_o}$

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.

CALCULATION:

Given QA = q, and QB = 2q

Where AA and AB = surface area of the cube A and the cube B respectively

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,

$\Rightarrow ϕ=\frac{Q}{ϵ_o}$      -----(1)

By equation 1 the total flux associated with cube A is given as,

$\Rightarrow ϕ_A=\frac{Q_A}{ϵ_o}$

$\Rightarrow ϕ_A=\frac{q}{ϵ_o}$      -----(2)

By equation 1 the total flux associated with cube B is given as,

$\Rightarrow ϕ_B=\frac{Q_B}{ϵ_o}$

$\Rightarrow ϕ_B=\frac{2q}{ϵ_o}$      -----(3)

By equation 2 and equation 3,

$\Rightarrow \frac{ϕ_A}{ϕ_B}=\frac{q}{ϵ_o}\times\frac{ϵ_o}{2q}$

$\Rightarrow \frac{ϕ_A}{ϕ_B}=\frac{1}{2}$

• Hence, option 1 is correct.