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.
