Question

A charge of 1 uC is situated at the center of a hollow
sphere of radius 2 m. If the radius of the sphere
reduces to 1 m without any shift in its center, then the
electric flux through the sphere would
Decrease by a factor of 2
Increase by a factor of 2
Remain unchanged
Reduce by a factor of 4​

Answer 1

Answer:

Electric flux through the sphere would remain unchanged.

Explanation:

Electric flux through a gaussian sphere is given by, $\phi = \frac{q_{enclosed}}{\epsilon_0}$

where, $q_{enclosed}$ is the charge enclosed inside the gaussian surface.

Initially, when radius of sphere is 2m,

Flux through the sphere = $\phi = \frac{q_{enclosed}}{\epsilon_0} = \frac{1\mu C}{\epsilon_0}$

later, when radius reduced to 1m,

Flux through the sphere = $\phi = \frac{q_{enclosed}}{\epsilon_0} = \frac{1\mu C}{\epsilon_0}$

Flux through both the sphere is same.

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