The insulation property of air breaks down at 3 × 106V/m. The maximum charge that can be given to a sphere of diameter 5 m is nearly

Question

The insulation property of air breaks down at 3 × 106V/m. The maximum charge that can be given to a sphere of diameter 5 m is nearly (A) 2 × 102C (B) 2 × 103C (C) 2 × 104C (D) 2 × 105C

Tardigrade Admin · Accepted Answer

Maximum electric field, Emax=(1/4πε0) (Qmax/R2) 3×106=(9×109× Qmax/2.5×2.5) or Qmax=(3×106×2.5×2.5/9×109) =2×10-3 C

Q. The insulation property of air breaks down at $3 \times 1 0^{6} V / m$ . The maximum charge that can be given to a sphere of diameter $5 m$ is nearly

$2 \times 1 0^{2} C$

$2 \times 1 0^{3} C$

$2 \times 1 0^{4} C$

$2 \times 1 0^{5} C$

Maximum electric field, $E_{ma x} = \frac{1}{4 π ε _{0}} \frac{Q _{ma x}}{R ^{2}}$
$3 \times 1 0^{6} = \frac{9 \times 1 0 ^{9} \times Q _{ma x}}{2.5 \times 2.5}$
or $Q_{ma x} = \frac{3 \times 1 0 ^{6} \times 2.5 \times 2.5}{9 \times 1 0 ^{9}}$
$= 2 \times 1 0^{- 3} C$

Q. The insulation property of air breaks down at 3×106V/m. The maximum charge that can be given to a sphere of diameter 5m is nearly

2×102C

2×103C

2×104C

2×105C