First slide

Gauss's Law

Question

In the arrangement shown in figure, electric flux through the closed surface 1 is Φ, through the closed surface 2 is 2Φ and through the closed surface 3 is 3Φ. Then the electric flux through a closed surface which encloses the charges Q₁ and Q₂ and Q₃ will be

Moderate

A

4Φ
B

3.5Φ
C

45Φ
D

3Φ

Solution

For surface 1, Q₁ + Q₂ = $\in_{o} . ϕ$
For surface 2, Q₂ + Q₃ = $\in_{o} . 2 ϕ$
For surface 3, Q₃ + Q₁ = $\in_{o} . 3 ϕ$
Adding, 2(Q₁ + Q₂ + Q₃)= $\in_{o} . 6 ϕ$
$\Rightarrow$ Q₁ + Q₂ + Q₃= $\in_{o} . 3 ϕ$
$\Rightarrow ϕ' = \frac{1}{\in_{o}}$ (Q₁ + Q₂ + Q₃) = $3 ϕ$ .

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