A transmission line strung 3.00 meters above the ground carries a current of 335 amps. What is the magnetic field on the ground directly below the wire?
So we have a transmission line 3.0 meters above ground that carries a current 𝐼 of 335 amps. Knowing all that, we want to solve for the strength of the magnetic field on the ground directly below this wire.
If we approximate this current carrying wire as an infinitely long straight line, then we can say that the magnetic field at perpendicular distance 𝑟 from the wire is equal to the permeability of free space 𝜇 nought times the current in the wire, all divided by two times 𝜋 times that distance 𝑟.
𝜇 nought the permeability of free space is a constant value. And we can treat it as exactly 1.26 times 10 to the negative sixth tesla meters per ampere. We know 𝜇 nought then. And we also know the current 𝐼 given as 335 amps as well as the distance 𝑟 of 3.00 meters.
When we plug in all these values, notice that the units of meters cancel out as do the units of amperes, leaving us with the units of tesla for our final answer. Our result to three significant figures is 2.24 times 10 to the negative fifth tesla. That’s the strength of the magnetic field due to this transmission line directly below the line on the ground.