- #1

shj

- 4

- 1

This is probably my misunderstanding, so please clarify.

In a region of empty space, there are

**two point charges**with the charges+Q and -Q. Exactly in the middle of the two charges (distance r from both charges) is

**point P**, colinear with the centers of both charges. A Gaussian surface that includes point P is drawn above.

Using Coulomb's Law, we can find the

**electric field at point P**:

*E=2*((1/4πε*_{0})Q/r^{2})=**(1/2πε**_{0})Q/r^{2})(since the electric field vectors caused by both charges have the same magnitude and add at point P)

However, if I try to use Gauss's Law to calculate the electric field at point P, I get:

*, or*

**E*4πr**^{2}=Q_{enclosed}/ε_{0}

*E=***(1/4πε**_{0})Q/r^{2})(since the Gaussian surface is symmetric to the electric field, I simplified the surface integral to E*4πr

^{2})

The two calculations differ! Can someone please clarify the error?!