Question

During electrical storms, a bolt of lightning can transfer 10 C of charge in 2.0 µs (the amount of time can vary considerably). We can model such a bolt as a very long current carrying wire. a. What is the magnetic field 1.0 m from such a bolt? What is the field at 1.0 km away? b. How do the field compare with Earth’s magnetic field?

Answer 1

Answer:

Explanation:

charge, q = 10 C

time, t = 2 micro second

Current, i = q / t

i = 10 / (2 x 10^-6) = 5 x 10^6 A

(a)

distance, d = 1 m

the formula for the magnetic field is given by

$B = \frac{\mu_{0}}{4\pi}\frac{2i}{d}$

$B = 10^{-7}\frac{2\times 5\times 10^{6}}{1}$

B = 1 Tesla

Now the distance is d' = 1 km = 1000 m

$B' = \frac{\mu_{0}}{4\pi}\frac{2i}{d}$

$B' = 10^{-7}\frac{2\times 5\times 10^{6}}{1000}$

B' = 0.001 Tesla

(b) The magnetic field of earth is Bo = 3 x 10^-5 tesla

B / Bo = 3.3 x 10^4

B'/Bo = 33.3