At one time, concern was raised about the possible health effects of the small a

Question

At one time, concern was raised about the possible health effects of the small 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 that melt and break the circuit if this current is exceeded). The two wires in a home power cord are about s = 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).

Calculate the maximum magnitude of the alternating magnetic field, d = 64 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.
T
(The magnitude of the field that you calculate is very small compared to the Earth's magnetic field, but there were questions as to whether a very small alternating magnetic field might have health effects. After many detailed studies, the consensus of most scientists now seems to be that these small alternating magnetic fields are not a hazard after all.)

Explanation / Answer

We know that the field due to one wire is given by:

B = u0 I/2 pi R

For the given system, the point at given point will be:

B = u0 I/ 2 pi [ 1/(d - s/2) - 1/(d + s/2))]

B = 4 pi x 10^-7 x 15 / 2 pi [ 1/(0.64 - 0.003/2) + 1/(0.64 + 0.003/2)] = 2.1 x 10^-8 T

Hence, B = 2.1 x 10^-8 T

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