Chapter 22, Problem 22.1DQ

A rubber balloon has a single point charge in its interior. Does the electric flux through the balloon depend on whether or not it is fully inflated? Explain your reasoning.

To determine

To Check: The electric flux through the balloon depends on whether or not it is fully inflated.

Explanation of Solution

The electric flux depends only on the charge present inside the rubber balloon and the electric constant.

Formula for electric flux using Gauss law,

${\Phi }_E=\frac{q}{{\epsilon }_0}$

• $q$ is the point charge in rubber balloon,
• ${\epsilon }_0$ is the electric constant.

From Gauss law, the flux does not depends on size of rubber balloon and therefore electric flux due to a point charge which is present inside the balloon will be equal to $\frac{q}{{\epsilon }_0}$.

The deflated balloon will not be in symmetry with a charge present inside and therefore it is difficult to calculate electric flux present in it.

Conclusion:

No, electric flux through the balloon does not depend on or whether it is fully inflated.