Gauss's Law## Example: Point Charge

Consider the E-field from a point charge Q and the flux through a sphere centered on that charge. By symmetry (there it is, again!) we know the E-field is radially outward (assuming the charge Q is positive) so it is

perpendicularto the surface. That means

EdA= E dA

So the integral over the surface is

And

Gauss's Lawis that this flux through the surface is equal to the charge enclosed by the surface divided by epsilon,Therefore,

Of course, this is just

Coulomb's Law. We would expect this since we started with Coulomb's Law when we "derived" Gauss's Law. The two are intimately connected!

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