A lightning bold strikes the ground 200m away from a 100 turn coil. Suppose that

Question

A lightning bold strikes the ground 200m away from a 100 turn coil. Suppose that the radius of the coil is .8 m and that the current carried by the lightning bolt is 6.0 MA and falls to zero in .0105s. What is the induced emf in the coil if it is oriented with its normal along the magnetic field direction? If the wire has a cross sectional area of 7 x 10-7 m2 (diameter of wire is .001m) and it is made out of copper                         ( =1.7 X 10-8 m), what is the magnitude and direction of the induced current in the wire?

Explanation / Answer

Number of turns is N = 100 Crosssectional area is A = 7*10^-7 m^2 Length is l = 200 m induced emf is e = L dI / dt      self inductance of the coil is L = _0 N^2 A /l                       = 4*10^-7 * ( 100)^2 *  7*10^-7 m^2 / 200                      = 43.9*10^-12 H           e = 43.9 *10^-12 H * d ( 6.0*10^6 A / 0.0105 s )               = 25.08*10^-3 V       resistance R = L / A                           = 1.7 *10^-8 m * 200 m / 7*10^-7 m^2                             = 4.85 current in the wire   i = e / R                                    = 25.08*10^-3 / 4.85                                   = 5.17 m A

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