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 in The figure below. What voltage is induced in a 1.00 m diameter loop 50.0 m from a 2.00 times 106 A lightning strike, if The current falls to zero in 44.6 mu s? What is The total energy carried by The short lightening strike, if The potential difference between The earth and The cloud is 3 times 106 volts (breakdown voltage of air)?

Explanation / Answer

induced emf : E = -(dB)(A) / dt

= - [(Mu0 * dI / 2 *pi * 50m) ( pi * r^2) ] / 44.6 * 10^-6

where dI = 2 * 10^6 A

a)

r = 0.5 ,
Mu0 = 4 * pi * 10^-7 T

Plugging in,

= [ ((4pi*10^-7 * 2*10^6) / (2pi*0.5)) (pi*0.5*0.5)] /44.6 * 10^-6
= 141 V

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