Answer:
1) q = 83.4 C
2)52.13 × 10^(19) electrons
Explanation:
1) To calculate the total charge q on the cloud when the breakdown of the surrounding air begins, we will use the formula;
E = kq/r²
Making q the subject, we have;
q = Er²/k
Where k is a constant = 1/(4πε_o)
We are given;
ε_o = 8.85 × 10^(-12)) C²/N.m²
Thus;
k = 1/(4 × π × 8.85 × 10^(-12)) N.m²/C²
k = 8.99 × 10^(9)
Also,we are given E = 3 × 10^(6) N/C
Diameter = 1km = 1000 m
Radius(r) = diameter/2 = 1000/2 = 500 m
Thus;
q = (3 × 10^(6) × 500²)/(8.99 × 10^(9))
q = 83.4 C
2) To get the number of Excess electrons, we will divide the charge gotten in Part 1 above by the charge of a single electron.
Now, charge of a single electron = 1.6 × 10^(-19) C
Thus, number of Excess elecrons = 83.4/(1.6 × 10^(-19)) = 52.13 × 10^(19) electrons
