Question

Radius of a spherical conductor is 2m, This is kept in dielectric medium of dielectric constant 10^6N//C. Find a. capacitance of the conductor b. maximum charge which can be stored on this conductor.

Answer 1

Given:

• Radius of a spherical conductor$(R) = 2m$

• Dielectric constant$= 10^6N / C$

To Find:  

            (a) Capacitance of the conductor

            (b) maximum charge which can be stored on this conductor.

Solution:

(a) Capacitance of the conductor  is given by

                                $C =\frac{R}{k}$

Putting the values,

                         $C =\frac{1}{9 \times 10^9} (2)$

                         C = $\frac{2}{9} \times 10^{-9}$

                         $C = 2.22 \times 10^{-8} F$

(b) Maximum electric field on the surface of spherical conductor is

                               $E = \frac{kq}{R^2}$

                              $E_(max) = \frac{kq}{R^2}$

   This should not exceed $10^6 N/C$

                         $E_(max) = \frac{kq_(max)}{R^2}$   $= 10^6 N/C$

                       $q_(max) =(4\pi \epsilon_0) R^2(10^6)$

                                    $=(\frac{1}{9 \times 10^9} )(2^2) (10^6)$

                        $q_(max) =4.4\times 10^{-4} C$

Thus, Maximum charge which can be stored on this conductor is $q_(max) =4.4\times 10^{-4} C$