A hemispherical surface with radius in a region of uniform

Chapter 22, Problem 22.5

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QUESTION:

A hemispherical surface with radius r in a region of uniform electric field \(\overrightarrow{\boldsymbol{E}}\) has its axis aligned parallel to the direction of the field. Calculate the flux through the surface.

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QUESTION:

A hemispherical surface with radius r in a region of uniform electric field \(\overrightarrow{\boldsymbol{E}}\) has its axis aligned parallel to the direction of the field. Calculate the flux through the surface.

ANSWER:

Step 1 of 2

Hemisphere and direction of electric field is sketched

The electric field line passes through the flat surface and also passes through the curved surface. The flux through the curved upper half of the hemisphere is the same as the flux through the flat

circle defined by the bottom of the hemisphere because every electric field line that passes through the flat circle also must pass through the curved surface of the hemisphere.

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