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. For a line that has current 150 A and a height of 8.0 m above the ground, what magnetic field does the line produce at ground level? Express your answer in teslas and as a percentage of the earth's magnetic field, which is 0.50 G. Is this value cause for worry?

Video transcript

Welcome back everybody. We are studying static magnetic fields and therefore place a Tesla meter 15 m away from a transmission line. We're told that this transmission line is carrying a steady current of 100 amps and we are tasked with finding what is the magnitude of the magnetic field and then what is the ratio between the magnetic field that we find in part one to the magnetic field at the university campus which we are told is to be 50 micro Tesla. So we'll have some number. We find a part one divided by that. Alright, so let's go ahead and start with part one here. So in order to find the magnitude of the magnetic field we have a formula for this. This is going to be mu not times our current, all divided by two pi times our distance. So let's go ahead and plug in our values here we have four pi times 10 to the negative seven times 100 amps. All divided by two pi times m. This gives us 1.33 times 10 to the negative six Tekla Tesla or 1.33 micro Tesla. Great. So now moving on to part B here, we need to find the ratio between our magnetic field in Part one to the magnetic field of the earth at the campus location. All we do is take our answer to Part one which is 1.33 micro Tesla guided by 50 micro Tesla and we get 0.226. Multiply this by 100 to achieve a percent and we get that the ratio between the two is 2.6%. So now we have found both the magnitude of the magnetic field coming off the transmission line, as well as the ratio between the two magnetic fields. And this gives us a final answer of answer choice. A thank you all so much for watching. Hope this video helped. We will see you all in the next one.