Question

Lightning occurs when there is a flow of electric charge (principally electrons) between the ground and a thundercloud.The maximum rate of charge flow in a lightning bolt is about20,000C/s; this lasts for$\mathbf{100}\mathbf{\mu s}$or less. How much charge flowsbetween the ground and the cloud in this time? How many electrons flow during this time?

Short answer

The charge flow between the ground and the cloud is 2.0 C. The electron flows during this time is $1.25\times {10}^{19}\mathrm{electron}$.

Step-by-step solution

Definition of the electric charge

Electric charge can exist only as an integral multiple of charge on an electron.The formula of the charge is given by,

$\mathit{Q}\mathbf{=}\mathbf{\pm }\mathit{N}\mathit{e}$

Here, Nis an integer, and eis the charge of the electron.

Calculation of the charge flow

Given that the rate of flow of the charge in the lighting is$r=20,000\mathrm{C}/\mathrm{s}$ for time $t=100\mu s$. The charge flow is given by the formula $Q=rt$.

Substitute the rate of flow and the time in the above formula to get a charge flow.

$$\begin{gathered} Q=20,000\mathrm{C}/\mathrm{s}\times 100\times {10}^{-6}\mathrm{s} \\ =2.0\mathrm{C} \end{gathered}$$

Hence, the charge flow between the ground and the cloud is 2.0 C.

Calculation of the flow of electrons

The number of electrons,$n_e$ is given by the formula $n_e=\frac{Q}{e}$.

Substitute the charge flow$Q=2.0\mathrm{C}$ and the charge of electron$e=1.60\times {10}^{-19}\hspace{0.17em}\mathrm{C}$ in the above formula to get the number of electrons.

$$\begin{gathered} n_e=\frac{2.0}{1.60\times {10}^{-19}\mathrm{C}} \\ =1.25\times {10}^{19}\mathrm{electron} \end{gathered}$$

Hence, the electron flows during this time is $1.25\times {10}^{19}$electron .