Respuesta :
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.
a) The magnetic field due Lightning bolt will be 8.16×10⁻⁴ T
b)The magnetic field due to household current will be 4.08×10⁻⁵ T
What is a magnetic field?
It is the type of field where the magnetic force is obtained. With the help of a magnetic field. The magnetic force is obtained it is the field felt around a moving electric charge.
The number of magnetic flux lines on a unit area passing perpendicular to the given line direction is known as induced magnetic field strength .it is denoted by B.
a) The magnetic field due Lightning bolt will be 8.16×10⁻⁴ T
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
[tex]\rm B_1= \frac{\mu_0i_1}{2 \pi r} \\\\ \rm B_1= \frac{4 \pi \times 10^{-7} \times 20,00}{2 \times 3.14 4.9} \\\\ \rm B_1= 8.16 \times 10^{-4} \ T[/tex]
b) Magnetic field due to household current will be 4.08×10⁻⁵ T
[tex]\rm B_2= \frac{\mu_0i_2}{2 \pi r} \\\\ \rm B_2= \frac{4 \pi \times 10^{-7} \times 10}{2 \times 3.14 0.049} \\\\ \rm B_2= 4.08\times 10^{-5} \ T[/tex]
Hence the magnetic field due to household current will be 4.08×10⁻⁵ T
The magnetic field created by lightning bolt current divided by the magnetic field produced by home electricity equals
[tex]\rm \frac{B_1}{B_2} = \rm \frac{8.16 \times 10^{-4}}{4.08 c\times 10^{-5}} \\\\ \rm \frac{B_1}{B_2} = 20 \\\\[/tex]
That is, the magnetic field created by a lightning bolt current is 20 times stronger than the magnetic field produced by a home current.
Hence the magnetic field due to the Lightning bolt will be 8.16×10⁻⁴and the magnetic field due to household current will be 4.08×10⁻⁵ T.
To learn more about the magnetic field refer to the link;
https://brainly.com/question/19542022
