First slide

Gauss's Law

Question

in a region of space electric charge in uniformly distributed throughout the volume. A cube of edge length l is placed in the region and electric flux from the entire surface of the cube is found to be Φ. If a cube of edge length 3l is placed to that region, the electric flux from the surface of the cube will be

Moderate

A

27 Φ
B

9 Φ
C

3 Φ
D

Φ

Solution

If Φ be the charge enclosed by the cube of edge length l, then Q = $ρ$ l³ where p is the change density.
$∴ ϕ' = \frac{Q}{\in_{0}} = \frac{ρ}{\in_{0}} l^{3} ∴ ϕ' = \frac{Q'}{\in_{0}} = \frac{ρ {(3 l)}^{3}}{\in_{0}} = 27 . ϕ$

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