Answer to Question #203066 in Electric Circuits for Nabeel khan

Question

An uncharged conducted spherical shells placed in the electric field of positive charge (q). What will be the net flux through the shell. What is the SI unit of electric flux?

Answer 1

Electric Flux through a surface is defined as the surface integral of the electric field lines passing normally through the surface.

$\phi=\intop E.ds$

According to gauss's law, total electric flux through a closed surface equals the net charge enclosed in the surface divided by the permittivitty.

Consider a point charge q. Its net electric flux through any closed surface enlcosing it will be be equal to

$\phi =\frac{q}{\epsilon_0}$

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This is independent of the choice of the shape and size of the closed surface.

The SI unit of electric flux is Volt - metres (V m)

For example

For charged spherical shell, all charge lies on the outer circumference of the surface.

Consider a charged spherical shell with outer radius b and inner radius a. The charge resides at a radius b from the centre. Consider a gaussian surface of radius a<r<b. Charge enclosed in this guassian surface will be zero.

Using gauss's law,

$\intop E.ds=\frac{q}{\epsilon_0}$

enclosed

E×2πrdr=0

Where r lies

$a<r<b$

E=0