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25 March, 00:51

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.

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  1. 25 March, 02:29
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    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.
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