Magnetic fields in the home At one time, concern was raised about the possible h

Question

Magnetic fields in the home
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).

(a) Calculate the maximum magnitude of the alternating magnetic field, d = 48 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.
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(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.)

(b) 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

The max field due to one wire would be

B = mu0 I/(2 pi r)

A current of size I is flowing at a distance r + d/2 of the point, whilst an opposite current flows at distance r - d/2 , with d the distance between the wires and r the distance from the middle of the wires to the point in question. The field will point out of the page.
So here

B = mu0 I/(2 pi) * ( 1/ (r-d/2) - 1/(r+d/2) )

B = 4 pi* 10^-7 H/m* 15 A/(2 pi) * ( 1/(0.48m - 0.0015m) - 1/(0.48m+0.0015m))
= 3.9*10^-8 T Ans.


If you twist the pair of wires the field will be much lower because the current in one direction is not always closer or further than the opposite current.

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