Question

A charge is uniformly distributed on the surface of a spherical rubber balloon. As it is blown up, the total electric flux coming out of the surface

• A. (decreases.)
• B. (increases.)
• C. (remains unchanged.)
• D. (becomes zero.)

Hint:

Flux depends on the amount of charge enclosed, not the volume of the enclosure.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks about the change in total electric flux through a surface when the surface expands, but the charge it encloses remains the same.
Step 3: Detailed Explanation:
According to Gauss's Law, the total electric flux \(\Phi\) through any closed surface is given by:
\[ \Phi = \frac{Q_{\text{enclosed}}}{\epsilon_{0}} \]
The law states that the flux depends only on the net charge enclosed by the surface and not on the shape or size of that surface.
When the rubber balloon is blown up, its surface area increases, but the total amount of charge residing on its surface (which is the charge "enclosed" if we consider a Gaussian surface slightly larger than the balloon) remains constant.
Since \(Q_{\text{enclosed}}\) is constant, the total electric flux \(\Phi\) remains unchanged.
Step 4: Final Answer:
The total electric flux remains unchanged.