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Currents in dc transmission lines can be 100 A or higher. Some people areconcerned that the electromagnetic fields from such lines near their homes could pose health dangers. For a line that has current 150A and a height of 8 m above the ground, what magnetic field does the line produce at ground level? Express your answer in tesla and as a percentage of the earth’s magnetic field, which is 05 G . Is this value cause for worry?

Short Answer

Expert verified

The magnetic field of earth has a magnitude of aboutB=5×10-5T , so the field produced by the transmission line is 7.5 % of the Earth’s magnetic field.

Step by step solution

01

The formula to be used in the problem

We need to find the magnetic field at the ground due to a transmission line that has current ofI=150A at a height ofr=8m above the ground. We will treat the line as a very long and straight wire.

The magnetic field due to a very long wire is given byB=μ0I2πr .

02

Find the magnetic field using the formula

B=μ0I2πrB=2×107×1508B=3.8×106T

The magnetic field of earth has a magnitude of aboutB=5×10-5T , so the field produced by the transmission line is 7.5 % of the Earth’s magnetic field.

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