Question

If you were unfortunate enough to be 5.5 mm away from such a lightning bolt, how large a magnetic field would you experience

Answer 1

The question is incomplete. Here is the complete question.

Lightning bolts can carry currents up to approximately 20kA. We can model such a current as the equivalent of a very long, straight wire.

(a) If you were unfortunate enough to be 5.5m away from such a lightning bolt, how large a magnetic field would you experience?

(b) How does this field compare to one you would experience by being 5.5cm from a long, straight household current of 5A?

Answer: (a) B = 7.27 x 10⁻⁴ T

(b) Approximately 40 times higher than a household one.

Explanation: Using Biot-Savart Law, the magnetic field in a straight, long wire is given by

`B=(\mu_(0)I)/(2.\pi.r)`

where:

`\mu_(0)` (permeability of free space) =
`4.\pi.10^(-7)`T.m/A

(a) If lightning bolt is compared to a long and straight wire, then magnetic field is

`B=(4.\pi.10^(-7).10.10^(3))/(2.\pi.5.5)`

B = 7.27 x 10⁻⁴ T

The magnitude of magnetic field in a lightning bolt is 7.27 x 10⁻⁴ T

(b) Magnetic field in a household wire will be

`B=(4.\pi.10^(-7).5)/(2.\pi.5.5.10^(-2))`

B = 1.82 x 10⁻⁵ T

Comparing fields:

`(7.27.10^(-4))/(1.82.10^(-5))` ≈ 40

The filed for a lightning bolt is approximately 40 times higher than for a household wire.