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Many physics textbooks say,

Gauss' law shows that the electric field inside a sphere with uniform charge distribution on the surface equals zero.

What I want to know is, do they mean total, i.e. the sum of all electric fields, and if so, at any point inside the sphere (except the center), is there a net electric field?

Kyle Kanos
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Gauri
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    Hi Gauri, and welcome to Physics Stack Exchange! We prefer to have one question per post, so I've removed the second question. Feel free to post it separately. – David Z Jul 12 '15 at 16:44
  • Possible duplicates: http://physics.stackexchange.com/q/150238/2451 and links therein. – Qmechanic Jul 12 '15 at 16:56
  • @ David Z It would have been so much kinder if you had allowed me to bifurcate the question or done so yourself. I've forgotten what the second question was and would hope that you had the time to remember it since you had the time to delete it. – Gauri Jul 13 '15 at 09:39

3 Answers3

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The statement means that the net electric field at any given point inside the sphere adds up to zero due to all the varying contributions by the charges on the surface. They exactly cancel out, and hence for any point inside the sphere, the value of electric field is exactly zero.

Pratik Rath
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This question is answered in the Wikipedia article on the shell theorem. The gist is that it is not the total.

But going beyond that, I think your question actually reflects a misunderstanding of what "electric field" means. The electric field is something which has a value at every point in space. If you try to calculate a total, e.g. by integrating the electric field over some region, the quantity you get is not electric field anymore. (If you integrate over a surface, the thing you get is called electric flux.) So when textbooks talk about the electric field being zero, they automatically mean that it is zero at every point in the region.

For comparison, you can also find cases where the electric flux - again, that's the "total" of electric field over a surface - is zero, but the electric field is not zero at every point on the surface. You'll see that textbooks actually use the word "flux", not "field", when they are talking about the thing that is zero. (Or they should, anyway.)

David Z
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If the shell is perfectly spherically symmetric, and the charge is perfectly evenly distributed on it, then the total field due to every singel charge is zero at every single point inside the sphere.

This also happens with gravity, there is no gravitational force inside a uniformly distributed shell of mass due to the shell of mass. While each piece of mass or charge might be responsible for a force, the vector sum of the forces due to each piece of mass or charge adds up to zero. At the center this is easy to see because there each piece has a piece on the opposite side that exactly cancels it. For locations off the center is isn't so obvious but still holds.

Timaeus
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