First slide

Gauss's Law

Question

A region of space contains some, charge uniformly distributed through out the space. When a spherical Gaussian surface of radius R is placed in the region electric flux through its surface is 12 volt-m. When a spherical Gaussian surface of radius 2R is placed in that region, electric flux through its surface will be

Moderate

A

24 V-m
B

36 V-m
C

96 V-m
D

48 V-m

Solution

Charge enclosed by a spherical Gaussian surface of radius R is Q = $\frac{4}{3} {πR}^{3} ρ$
$∴$ Charge enclosed by a spherical Gaussian surface of radius 2R is, $Q' = {(\frac{2 R}{R})}^{3} Q = 8 Q$
By Gauss's law, Flux $(ϕ) \propto Q_{net}$
$∴ \frac{ϕ}{12} = \frac{8 Q}{Q} \Rightarrow ϕ = 96$ volt-m.

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