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 about 20,000 C/s this lasts for 100 μs or less.
1.How much charge flows between the ground and the cloud in this time? (Q= ? C)
2.How many electrons flow during this time? (n_e = ? )

Answer 1

Concepts and reason

The main concepts used to solve this problem are electric charge and the numbers of electron.

Initially, From the definition of the current determine the how much charge flows. Later from the definition of the charge it is easy to determine the number of the charge.

Fundamentals

From the definition of the current, it is defined as the rate of change of current.

The expression of the current is equal to,

$I = \frac{{dq}}{{dt}}$

Here, $I$ is the current, $q$ is the charge and $t$ is the time.

The expression of the number of the charge is equal to,

$q = ne$

Here, $q$ is the number of the charge, $n$ is the number of the charge and $e$ is the charge of electron.

(1)

Calculate how much charge flows between the ground and a thundercloud.

The expression of the charge flows between the ground and a thundercloud is expresses as follows,

$I = \frac{q}{t}$

Rearrange the above expression in term of the charge,

$q = It$

Substitute $20000 {\rm{C/s}}$ for $I$ and $100 {\rm{\mu s}}$ for $t$ in the above expression of the charge,

$\begin{array}{c}\\q = \left( {20000 {\rm{C/s}}} \right)\left( {100 {\rm{\mu s}}} \right)\\\\ = \left( {20000 {\rm{C/s}}} \right)\left( {100 {\rm{\mu s}}} \right)\left( {\frac{{1 {\rm{s}}}}{{1000000 {\rm{\mu s}}}}} \right)\\\\ = 2 {\rm{C}}\\\end{array}$

(2)

Calculate the number of the electron flow during this time.

Rearrange the above expression of the charge in terms of the number of the elector.

$n = \frac{q}{e}$

Substitute $2 {\rm{C}}$ for $q$ and $1.6 \times {10^{ - 19}} {\rm{C}}$ for $e$ in the above expression of the number of the charge.

$\begin{array}{c}\\n = \frac{{2 {\rm{C}}}}{{1.6 \times {{10}^{ - 19}} {\rm{C}}}}\\\\ = 1.25 \times {10^{19}}\\\end{array}$

Ans: Part 1

The number of charge flows between the ground and a thundercloud is equal to $2 {\rm{C}}$ .
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Part 2

The number of the electron flowing this time is equal to $1.25 \times {10^{19}}$ .