A lightning bolt produces a rapidly varying magnetic field. If the bolt strikes

Question

A lightning bolt produces a rapidly varying magnetic field. If the bolt strikes the earth vertically and acts like a current in a long straight wire, it will induce a voltage in a loop aligned like that shown in the figure below. What voltage is induced in a 0.90 m diameter loop 45.0 m from a 2.00106 A lightning strike, if the current falls to zero in 25.0 ?s? (Discuss circumstances under which such a voltage would produce noticeable consequences.)

A lightning bolt produces a rapidly varying magnetic field. If the bolt strikes the earth vertically and acts like a current in a long straight wire, it will induce a voltage in a loop aligned like that shown in the figure below. What voltage is induced in a 0.90 m diameter loop 45.0 m from a 2.00½106 A lightning strike, if the current falls to zero in 25.0 ?s? (Discuss circumstances under which such a voltage would produce noticeable consequences.)

Explanation / Answer

induced emf is defiend as the rate of change of magnetic flux

in mathematical form,

induced emf e = NAdB/dt

where A = area

N = no. of tunrs

dB/dt = rate of change of amgnetic flux

so magnetic filed B = u0i/2pIr

B = 4pie-7* 2e6/(2pi* 45)

B = 8.89 *10^-9 T

so emf e = 1* 3.14*(0.45*0.45) * 8.89e-9/25e-6

emf e = 0.226 mV

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