Question

How much positive charge should be given to the earth so as to have the same potential as that of a positively charged sphere of $1 \, μC$ and radius $1 \, cm$ . (Radius of earth $=6400 \, km$ )

• A. $600 \, C$
• B. $640 \, C$
• C. $340 \, C$
• D. $240 \, C$

Answer 1

Answer: (B)

For potential of two spheres to be same,
$\frac{k q_{1}}{r_{1}}=\frac{k q_{2}}{r_{2}}$
or $\frac{q_{1}}{r_{1}}=\frac{q_{2}}{r_{2}}$
$\frac{q_{1}}{6400 \times 1 0^{3}}=\frac{1 \times 1 0^{- 6}}{1 0^{- 2}}$
$q_{1}=640 \, C$