Extra Credit: At one time, concern was raised about the possible health effects

Question

Extra Credit: At one time, concern was raised about the possible health effects of the sma alternating (60 hertz) magnetic fields created by electric currents, in houses and near power lines. In a house, most wires carry a maximum of 15 amperes (there are 15 ampere fuses break the circuit if this current is exceeded). The two wires in a home po - 3 millimeters apart, as shown in the figure, and at any instant they carry currents in opposite directions (both of which change direction 60 times per second). that melt and wer cord are al out s Side view I in I out Top view (a) Calculate the maximum magnitude of the alternating magnetic field, d 50 cm away from the center of a long straight power cord that carries a current of 15 amperes. Both wires are at the same height as the observation location. (b) Explain what, if anything, you can conclude from your result about this being a potential hazard. What other tests could you do? (c) Twisting the pair of wires into a braid as shown would minimize the magnetic field at the location discussed in (a). Do you see why?

Explanation / Answer

Given,

x = 3 mm ; d = 50 cm ; I = 15 A

a)The magnetic field at the distance d because of the current in the wire will be given by:

B = uI/2pi(1/d1 - 1/d2)

d1 = (d - x/2) = 0.5 - 0.0015 = 0.4985

d2 = (d + x/2) = 0.5 + 0.0015 = 0.5015 m

B = 4 pi x 10^-7 x 15/2 pi (1/0.4985 - 1/0.5015) = 3.6 x 10^-8 T

Hence, B = 3.6 x 10^-6 T

b)The value of B field calculated is small for causing health hazards to human.

c)The B field gets lowered significantly since the distance of point from the wires keep chaging.

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