Question

Lightning bolts can carry currents up to approximately 20 kA. We can model such a current as the equivalent of a very long, straight wire. You may want to review (Pages 926 - 929) . For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Magnetic field of a single wire. Part A If you were unfortunate enough to be 4.9 m away from such a lightning bolt, how large a magnetic field would you experience? Express your answer using two significant figures. B1 = nothing T Request Answer Part B How does this field (B1) compare to one (B2) you would experience by being 4.9 cm from a long, straight household current of 10 A? Express your answer using two significant figures.

Answer 1

Given Information:

Current due to Lightning bolt = I₁ = 20 kA

Current of household = I₂ = 10 A

Distance = r₁ = 4.9 m

Distance = r₂ = 4.9 cm = 0.049 m

Required Information:

a) Magnetic field due Lightning bolt = B₁ = ?

b) Magnetic field due to household current = B₂ = ?

Answer:

a) Magnetic field due Lightning bolt = B₁ = 8.16×10⁻⁴ T

b) Magnetic field due to household current = B₂ = 4.08×10⁻⁵ T

B₁ = 20B₂

Explanation:

The magnetic field produced in a long straight wire carrying a current (I) at distance r is given by  

B = μ₀I/2πr  

Where μ₀ is the permeability of free space and its value is 4π×10⁻⁷

a) The magnetic field produced due to the lightning bolt current is

B₁ = μ₀I₁/2πr₁

B₁ = (4π×10⁻⁷*20,000)/2π*4.9

B₁ = 0.000816

B₁ = 8.16×10⁻⁴ T

Therefore, the strength of magnetic field due to the lightning bolt current is 8.16×10⁻⁴ T

b) The magnetic field produced due to the household current is

B₂ = μ₀I₂/2πr₂

B₂ = (4π×10⁻⁷*10)/2π*0.049

B₂ = 0.00004081

B₂ = 4.08×10⁻⁵ T

Therefore, the strength of magnetic field due to the household current is 4.08×10⁻⁵ T

The ratio of magnetic field produced by the lightning bolt current to the magnetic field produced by the household current is

B₁/B₂ = 8.16×10⁻⁴/4.08×10⁻⁵

B₁/B₂ = 20

B₁ = 20B₂

Which means that the magnetic field produced by the lightning bolt current is 20 time greater than the magnetic field produced by the household current.