Question

After several damaging lightning strikes during midwestern summer thunderstorms, you've decided to protect your house by setting up an iron lightning rod. The lightning rod is 6.0 meters tall, with the top sharpened to a point and the bottom in good contact with the ground. After some googling, you've determined that lightning bolts typically carry about 30,000 amps of current and last around 60 microseconds. a. Assuming that you can trust the internet, how much charge is delivered by a typical lightning bolt? b. If you want the potential difference between the top and bottom of the lightning rod to be less than 100 V, what is the minimum radius of the rod?

Answer 1

THe given details are

Length of the rod, L = 6m

current, I = 30000 A

time , t = 60 micro seconds

t = 60*10^-6 s

in addition to that

resistivity of iron

$\rho$ = 9.70 * 10^-8$\Omega$m

(a) Charge stored, Q = I*t

Q = 30000*60*10^-6

Q = 1.8 Coulomb

(b) By ohms law

potential difference

V = I*R (1)

R = ($\rho$L/A) (2)

where A is the area of cross section

A = $\pi$ r²

Therefor Equation (1) becomes

V= I* ($\rho$L/A)

100 = 30000*(9.70*10^-8 *6 / $\pi$ r²)

r² = (30000*9.70*10^-8 *6)/ 100 $\pi$

r² = 5557.69*10-8 m

r = 7.455 mm

Result

if we want to potential difference is less than 100 v

The radius of the rod must be greater than 7.455 mm

From the equation it is clear that V and r is in inversly proportional