Question

There is one hollow sphere of radius 1 m and it contains
a charge of 8.85 uC at its centre. Calculate the electric
flux linked with the sphere per unit area. Electric flux
per unit area is defined as flux density.​

Answer 1

Given :

The radius of the sphere = 1 cm

The charge contained in the sphere = 8.85μC

To Find :

The electric flux linked with the sphere per unit area

Solution :

• According to Gauss law the electric flux linked with the sphere containing charge ‘q’ in it is given by

             $Electric\:flux=\frac{q_{in}}{\epsilon_{0}}$

             $Electric\:flux=\frac{8.85\times10^{-6}}{8.85\times10^{-12}}$

             $Electric \:flux = 10^{6}\:Nm^{2}/C$

• Electric flux density is defined as the electric flux per unit area

           $Electric\: flux \:density =\frac{Electric\:flux}{Area}$

           $Electric\: flux \:density =\frac{10^{6}}{4\pi r^{2}} = \frac{10^{6}}{4\pi(1)^{2}}$

           $Electric\:flux\:density = 7.957 \times10^{4} N/C$

The electric flux density of the sphere is 7.957×10⁴ N/C