Question

Currents in dc transmission lines can be 100 A or higher. Some people are concerned that the electromagnetic fields from such lines near their homes could pose health dangers.

Part A

For a line that has current \(180 \mathrm{~A}\) and a height of \(8.0 \mathrm{~m}\) above the ground, what magnetic field does the line produce at ground level? Express your answer in teslas.

Part B

What magnetic field does the line produce at ground level as a percent of the earth's magnetic field, which is \(0.50 \mathrm{G}\).

Express your answer using two significant figures.

Part C

Is this value of magnetic field cause for worry?

No. Since this field is much smaller than the earth's magnetic field, it would be expected to have less effect than the earth's field.

Yes. Since this field is does not differ a lot from the earth's magnetic field, it would be expected to have almost the same effect as the earth's field. No. Since this field is does not differ a lot from the earth's magnetic field, it would be expected to have almost the same effect as the earth's field. Yes. Since this field is much greater than the earth's magnetic field, it would be expected to have more effect than the earth's field.

No. Since this field is does not differ a lot from the earth's magnetic field, it would be expected to have almost the same effect as the earth's field.

Yes. Since this field is much greater than the earth's magnetic field, it would be expected to have more effect than the earth's field.

Answer 1

Concepts and reason

The concepts required to solve the problem are the magnetic field due to current carrying wire, Earth’s magnetic field and the ratio of field due to the current carrying wire with Earth’s filed.

Determine the magnetic field due to the current carrying wire by using the current through the wire and the distance between the center of wire and the ground. Compare the magnetic field due to the current carrying wire with the magnetic field due to Earth by taking the ratio between them.

Check whether the magnitude of the magnetic field due to the current carrying wire is comparable with the magnitude of the magnetic field due to Earth to check the risk the magnetic field creates.

Fundamentals

The magnetic field at ground level due to the current carrying wire is,

Here, is the permeability of free space, is the current through the wire and is the distance of the center of wire from the ground.

(A)

The magnetic field at ground level due to the current carrying wire is,

Substitute for , for and for . The magnetic field at the ground level due to the current carrying wire is,

(B)

The percentage of the magnetic field due to the current carrying wire at the ground level to the Earth’s magnetic field is,

Substitute for and for . The percentage of the magnetic field due to the current carrying wire at the ground level to the Earth’s magnetic field is,

(C)

The statement ‘No. Since the field is much smaller than the Earth's magnetic field, it would be expected to have less effect than the Earth's field’ is correct. The magnetic field of the current carrying wire is only of the earth’s magnetic field and hence causes very less effect compared to magnetic field of Earth.

Ans: Part A

The magnetic field at the ground level due to the current carrying wire is .

Part B

The percentage of the magnetic field due to the current carrying wire at the ground level to the Earth’s magnetic field is .

Part C

No. Since the field is much smaller than the Earth's magnetic field, it would be expected to have less effect than the Earth's field.