You wonder if you could entirely support a clothesline by running an electric cu

Question

You wonder if you could entirely support a clothesline by running an electric current through it. Imagine you are in Costa Rica (perhaps for LCC's summer bio course) where the Earth's magnetic field is horizonatl. The line you'll need is about 10m long and you measure the Earth's magnetic field to be about 50µT. You also guess that the clothes will be a maximum of 25kg when wet.


What direction should you hang the line? What current would you need? Does this sound like a promising way to do this? Explain all answers.

Explanation / Answer

The magnetic field runs from south to north so you are going to orient your clothesline east-west so the current runs crossways to the field ... F = iL x B and you want the force to be directed upward so the current should run from west to east (right-hand rule).

Assuming we are perfectly perpendicular to the field, iL x B just becomes iLB (since sin 90 degrees is 1).

So how much force do we need? F = mg = (25 kg)(9.81 m/s) = 245 N which is what our iLB has to equal.

We know B = 50 T, L = 10 m; solving for i:

i = F/LB = 245 N/(10 m * 50 T) = 4.9 * 105 A or 490,000 amps, a ridiculously high amount of current that would instantly vaporize any clothesline-sized wire it ran through ... so, no this is not practical.

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