At one time, concern was raised about the possible health...

At one time, concern was raised about the possible health effects of the small alternating (60-Hz) magnetic fields created by electric currents in houses and near power lines. In a house, most wires carry a maximum of 15 A (there are 15 -A fuses that melt and break the circuit if this current is exceeded). The two wires in a home power cord are about $3 \mathrm{mm}$ apart as shown in Figure $17.87,$ 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, $50 \mathrm{cm}$ away from the center of a long straight power cord that carries a current of 15 A. Both wires are at the same height as the observation location. (b) Explain briefly why twisting the pair of wires into a braid as shown in Figure 17.88 greatly decreases the magnetic field at the location discussed in (a), a generally useful technique. (c) Optional: For two long parallel wires like those shown in part (a), a distance $d$ apart and carrying conventional current $I$ in opposite directions, find an algebraic equation for the magnetic field a perpendicular distance $r \gg d$ to the right of the wires. (The magnitude of the field that you calculated in part (a) 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.)

At one time, concern was raised about the possible health effects of the small alternating (60-Hz) magnetic fields created by electric currents in houses and near power lines. In a house, most wires carry a maximum of 15 A (there are 15 -A fuses that melt and break the circuit if this current is exceeded). The two wires in a home power cord are about $3 \mathrm{mm}$ apart as shown in Figure $17.87,$ 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, $50 \mathrm{cm}$ away from the center of a long straight power cord that carries a current of 15 A. Both wires are at the same height as the observation location. (b) Explain briefly why twisting the pair of wires into a braid as shown in Figure 17.88 greatly decreases the magnetic field at the location discussed in (a), a generally useful technique.
(c) Optional: For two long parallel wires like those shown in part
(a), a distance $d$ apart and carrying conventional current $I$ in opposite directions, find an algebraic equation for the magnetic field a perpendicular distance $r \gg d$ to the right of the wires. (The magnitude of the field that you calculated in part (a) 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.)

Key Concepts

Magnetic Field from a Long Straight Conductor

A long straight conductor carrying an electric current generates a magnetic field that encircles the wire. This field's magnitude is determined by Ampere's law, where the field strength is proportional to the current and inversely proportional to the distance from the conductor. This concept is critical when calculating the magnetic field at any point surrounding a power-carrying wire.

Superposition Principle

The superposition principle states that the net field at any point is the vector sum of the magnetic fields produced by individual sources. When multiple current-carrying wires are involved, especially with currents in opposite directions, their magnetic fields can partially or completely cancel each other out. This idea is essential for understanding how wire configurations affect the overall magnetic field in a region.

Wire Twisting and Field Cancellation

Twisting or braiding wires is a practical method to reduce stray magnetic fields. By regularly alternating the positions of the wires relative to each other, the magnetic fields produced by individual wires cancel out over short distances. This configuration minimizes external interference and reduces the net magnetic field, which is an important consideration in both electrical safety and electromagnetic compatibility design.

Alternating Current (AC) and Time-Varying Magnetic Fields

Alternating current (AC) periodically reverses its direction, causing the magnetic field produced by the current to also oscillate. This time-varying nature of the magnetic field is significant because it affects how the field interacts with its environment, including potential implications for interference and human exposure. Understanding AC behavior is crucial in analyzing systems where the current changes direction rapidly, such as in household electrical circuits.

Transcript

00:01 So for part a, we know that the strength of the magnetic field produced by a current carrying wire from the wire, at some distance from the wire, is 2 times 10 to the negative 7th times the current in the wire divided by the distance.

00:18 So we can say that the magnetic field would be 2 times 10 to the negative 7th tesla's meters per amps multiplied by the current.

00:31 Divided by the separation d.

00:33 And so we can say that then the magnetic field is equaling to 2 times 10 to the negative 7th, tesla's meters per amps.

00:44 This will be multiplied by 10 amps divided by half a meter.

00:50 And this is giving us 4 .0 times 10 to the negative 6th teslas.

00:57 Now, the strength of earth's magnetic field is equaling 5 .0 times 10 to the negative fifth, teslas.

01:08 So we can say that then b divided by b sub e is simply equaling 0 .08.

01:16 Therefore, the magnetic field in your house is only 8 % of the magnetic field due to earth.

01:27 So for part b, here now we have a power line essentially.

01:39 And so here the magnitude is equaling to 2 times 10 to the negative 7th teslas meters per amps and this will be multiplied by 200 amps divided by 20 meters high and this is giving us 2 .0 times 10 to the negative 6th teslas and as you can see we have 4 .0 times 10 to negative 6 teslas so essentially we can say that then the magnetic field from the transmission line is only equal to the magnetic field of your house divided by two.

02:32 And the reason why they do this is because the magnetic field is dependent more, of course, is dependent on the current and not the voltage.

02:43 So you can have really high voltages and not result in high magnetic fields, simply because the current is sufficiently low, such that the magnetic field is low as well.

03:00 Also, placing them 20 meters above the, placing them 20 meters high above the sidewalk is also beneficial in the sense that that also reduces the magnitude of the magnetic field that you're experiencing walking down the sidewalk.

03:18 For part c, we have that, that pregnancy magazines suggest that placing your baby within an electric blanket might not be comfortable, rather safe, simply because the magnetic fields induced through the electric blanket may harm the development of the baby...

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