**Goal:** Hone the concept of flux

**Source:** 283-400, Flux in and out of a balloon.

We construct a closed Gaussian surface in the shape of a sphericalWe construct a closed Gaussian surface in the shape of a spherical

balloon. Assume that a small glass bead with total charge Q is in the

vicinity of the balloon. Consider the following statements:

If the bead is inside the balloon, the electric flux over the

balloon’s surface can never be 0.If the bead is outside the balloon,

the electric flux over the balloon surface must be 0.

Which of these statements is valid?

- Only A is valid.
- Only B is valid.
- Both A and B are valid.
- Neither one is valid.

## Commentary:

## Answer

(3) Students may accept statement A but still think that the value of

the flux depends upon location of the bead in the sphere. Transition

from just inside to just outside poses particular difficulty to some

students. This usually derives from lack of experience with vectors and

dot products. Having the student draw field lines does help, but only

after they comprehend that the formal definition of flux is equivalent

to counting the net number of lines of E crossing the surface.