# Electric field, Coulomb's and Gauss' law

1. Can there be an electric field to the point where there is no charge? Can there be a charge at a place where there is no field? Please write a one or two sentence answer to each of these questions.

2. Let's say you are holding two tennis balls (one in each hand), and let's say that these balls each have a charge Q. estimate the maximum value of Q so that the balls do not repel each other so hard that you can't hold on to them.

3. A fresh "D cell" battery can provide about 5000 J of electrical energy before it must be discarded. Estimate the number of coulombs that muts pass through it during its lifetime.

#### Solution Preview

The second part of question 1 is rather complicated. I'm sure that was not intended by your Prof. However, to understand the issues here, it is necessary to consider this in full detail.

Can there be an electric field at a point where there is no charge?

Clearly, the answer is "yes". E.g., a point charge q has an electric field of E = q/(4 pi epsilon_0 r^2) in the radial direction. This field exists in the "empty space" surrounding the point charge.

Can there be a charge at a place where there is no field?

To address this question rigorously is a bit complicated because of the fact that charge is quantized, i.e. it always appears as a multiple of the elementary charge. At the exact point where the charge resides, the electric field is undefined if you use Coulomb's formula. Let's first look at this problem from a macroscopic point of view where you can pretend as if charge is a continuous quantity. Then, according to Gauss' Law, we have:

Surface integral of E dot dS = Q/epsilon_{0} (1)

Here the surface integral is over a closed surface, dS is a ...

#### Solution Summary

A detailed solution is given. Concepts covered in the problems include electric fields, Coulomb's law and Gauss' law.