Question

During storms clouds get changed. The dielectric breakdown of air is $3\times {10}^6$ V/m and there is a cloud of area $0.5k{m}^2$ which is 500 m above ground. This cloud induces an opposite charge on ground due to which this cloud-ground system behaves as a parallel plate capacitor.

• A. Minimum charge on cloud to produce lightning is 13.2 C.
• B. Total energy released in the process of lightning will be $9.9\times {10}^{9}J$.
• C. Minimum potential difference between cloud and ground to produce lightening $1500\times {10}^6$ volts.
• D. Maximum potential difference between clouds and ground can be $300\times {10}^6$ volts.

Answer 1

Answer: (A), (B), (C)

The correct options are
A Minimum charge on cloud to produce lightning is 13.2 C.
B Total energy released in the process of lightning will be $9.9\times {10}^{9}J$.
C Minimum potential difference between cloud and ground to produce lightening $1500\times {10}^6$ volts.

Since $Q=CV=\frac{{ϵ}_{0}A.Ed}{d}={ϵ}_{0}AE$

$Q=8.8\times {10}^{-12}\times 0.5\times {10}^6\times 3\times {10}^6=13.2C$

Energy = $\frac{Q^2}{2C}=\frac{Q^{2}d}{2{ϵ}_{0}A}=\frac{(13.2{)}^2\times 500}{2\times 8.8\times {10}^{-12}\times 0.5\times {10}^6}=9900\times {10}^{6}J$

$E=\frac{V}{d}\Rightarrow V=Ed=3\times {10}^6\times 500$
$=1500\times {10}^{6}V$