Question

How much positive charge should be given to the earth so that to have same potential that of a positively charged sphere of 1 micro coulomb and radius 1 cm. Radius of earth = 6400 km

Answer 1

Given:

Small sphere has 1 micro-C charge and is of radius 1 cm. Radius of Earth is 6400 km

To find:

Charge to be given to earth so as to have the same potential as that of the small sphere.

Calculation:

$\therefore \: \: P_{earth} = P_{sphere}$

$= > \dfrac{1}{4\pi\epsilon_{0}} \{\dfrac{q1}{r1} \} = \dfrac{1}{4\pi\epsilon_{0}} \{ \dfrac{q2}{r2} \}$

$= > \dfrac{1}{4\pi\epsilon_{0}} \{\dfrac{q1}{6400000} \} = \dfrac{1}{4\pi\epsilon_{0}} \{ \dfrac{1 \times {10}^{ - 6} }{0.01} \}$

$= > \cancel{ \dfrac{1}{4\pi\epsilon_{0}}} \{\dfrac{q1}{6400000} \} = \cancel{\dfrac{1}{4\pi\epsilon_{0}} } \{ \dfrac{1 \times {10}^{ - 6} }{0.01} \}$

$= > \dfrac{q1}{6400000} = \dfrac{1 \times {10}^{ - 6} }{0.01}$

$= > \dfrac{q1}{6400000} = {10}^{ - 4}$

$= > q1 = 6400000 \times {10}^{ - 4}$

$= > q1 = 640 \: C$

So final answer is :

640 C has to be given to Earth to get same potential as the smaller sphere.