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 )

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

Tardigrade Admin · Accepted Answer

For potential of two spheres to be same, (k q1/r1)=(k q2/r2) or (q1/r1)=(q2/r2) (q1/6400 × 1 03)=(1 × 1 0- 6/1 0- 2) q1=640 C

Q. 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 $1 μ C$ and radius $1 c m$ . (Radius of earth $= 6400 km$ )

$600 C$

$640 C$

$340 C$

$240 C$

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

Q. 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 1μC and radius 1cm . (Radius of earth =6400km )

600C

640C

340C

240C