If the electric flux through a closed surface is zero, is the electric field necessarily

Chapter 16, Problem 23Q

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QUESTION:

If the electric flux through a closed surface is zero, is the electric field necessarily zero at all points on the surface? Explain. What about the converse: If at all points on the surface is the flux through the surface zero?

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QUESTION:

If the electric flux through a closed surface is zero, is the electric field necessarily zero at all points on the surface? Explain. What about the converse: If at all points on the surface is the flux through the surface zero?

ANSWER:

Solution 23Q:

Step 1 of 2:-

Here we have to explain whether the electric field at the surface will be zero, if the flux through the surface is zero.

The electric field need not to be zero at the surface necessarily. The flux through a closed surface is zero means that, there is no charge present inside the closed surface.

Imagine a charge present outside a closed surface. In this case, the flux through the surface is zero, but the electric field at the surface is non-zero.

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