Respuesta :
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
[tex]B=\frac{\mu_{0}I}{2.\pi.r}[/tex]
where:
[tex]\mu_{0}[/tex] (permeability of free space) = [tex]4.\pi.10^{-7}[/tex]T.m/A
(a) If lightning bolt is compared to a long and straight wire, then magnetic field is
[tex]B=\frac{4.\pi.10^{-7}.10.10^{3}}{2.\pi.5.5}[/tex]
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
[tex]B=\frac{4.\pi.10^{-7}.5}{2.\pi.5.5.10^{-2}}[/tex]
B = 1.82 x 10⁻⁵ T
Comparing fields:
[tex]\frac{7.27.10^{-4}}{1.82.10^{-5}}[/tex] ≈ 40
The filed for a lightning bolt is approximately 40 times higher than for a household wire.
