The Charge Of A Lightning Bolt

Rate of flow of charge= 20kC/s = 20000 C/s = 2E4 C/s

Time for flow of charge = 100E-6 s

Charge on electron = 1.6E-19 C

Total flow of charge = (rate of flow of charge)(time for flow of charge) = (2E4)(100E-6) = 2C

Number of electrons = $\dfrac{\text{Total charge}}{\text{charge of electron}} = \dfrac{2}{\text{1.6E-19}} = \text{1.25E19 electrons}$

Rate of charge flow in a lightning bolt $=20$ kC/s $=20\times 10^3$ C/s

Time that the lightning bolt lasted $=100 \mu$ s $=100\times 10^{-6}$ s = $10^2\times 10^{-6} = 10^{2-6}=10^{-4}$ s.

Let the number of electrons that flow between the ground and the cloud duting the time of lightning bolt be $n$ . Now, we have--

(Total charge of the electrons during the flow) = (Rate of charge flow) * (Time of flow)

$\implies n\times$ (Charge of each electron) $= 20\times 10^3 \times 10^{-4}$

$\implies n\times 1.6\times 10^{-19}=2\times 10^4 \times 10^{-4}$

$\implies n=\frac{2}{1.6\times 10^{-19}}$

$\implies n=1.25\times 10^{19} = \boxed{1.25E+19}$

GIVEN

Rate of flow of charges=I=20kC/s=2E4 C/s

Time=t=100E-6 s

Charge on electron=e=1.6E-19 C

REQUIRED

No. of electrons=n=?

FORMULA+SOLUTION

We know by the definition of current:

           I=Q/t ................(1)

Here,

Q=No. of electrons*Charge on electron

i.e

   Q=n*e

Putting in equation (1) , we get:

              I=n*e/t

or,

             It/e=n

By putting values,

             n=2E-4 x 100E-6/1.6e-19

By calculation,

             n=1.25E19 electrons

Here,

Rate of flow = 20,000C / s

Time = 10E-4s

Therefore, charge = rate * time = 2C

1C = 6.25E+18 electrons

2C = 12.5E+18 electrons

Rate of flow of charge= 20kC/s Time=100 μs = 10^-4 s

Rate of flow of charge in the given time= 20000x10^-4 = 2C

No. of electrons= 2/1.6E-19 = 1.25E19