# Lighting an Electric Bulb with Earth's Magnetic Field

Yesterday, I was solving some problems of Electromagnetic Induction. Suddenly a thought struck my mind.

Earth has its own magnetic Field.If an aircraft of metallic body is flying in the air then across its wing a voltage must be induced by motional EMF. So, suppose if we connect a bulb across its wing (at extreme ends) will the bulb glow?

Generally, the wingspan of normal aircraft is 30m (but of Boeing 777 is 65m) and it normally travels with a speed of 700-800km/h or 225 m/s. The place where I live(New Delhi), vertical magnetic field component is approximately 50 microTesla. So, if we assume wing to a straight rod then EMF induced across wings must be

B.L.v =$$50\times10^{-6}\times65\times225$$= 0.72 volts

Appreciable potential difference. Small pencil LEDs typically get lit by mercury cell at 1.35 volts. But the point where I am having confusion is that the Earth magnetic field varies with the place.

So Will the bulb glow considering we have a bulb which can glow on a potential difference of this order, that is bulb consuming very low power ??

• Voltage does not make an LED glow. A sustained, sufficiently high voltage will make current flow in the LED, and the current will make the LED glow; but it takes power to sustain the voltage while the current is flowing. Your calculation needs to account for the power that is needed to keep the LED glowing. – Solomon Slow Mar 7 at 14:13
• @SolomonSlow A moving conductor at a level height from Earth's surface, moving at a constant velocity, through that part of Earth field which is not rotating can generate Electric Power. – Priyanshu Mar 7 at 15:56
• OK, but how much power? Enough to light a LED? A very low-power LED might require 2mA of current at 1.8V. That's 3.6mW of power. I do not know the equations that you are working with, but I do not see power or current anywhere in them. If your device can not generate a continuous 3.6mW of power, then it will not be able to continuously light an LED. Just knowing the open-circuit voltage that it can produce is not enough to tell you how much power it can produce. – Solomon Slow Mar 7 at 16:36
• We can write the power equation as $I^2/R$ .where I and R are respective physical quantities. Obviously, the Current varies as I stated in EDIT. Now, you stated that even if we work with a very low power LED or bulb of any other type, it would not be able to continuously light an LED as after few moments the acceleration of electrons would stop as Electric forces balance Magnetic Forces. But that would be applicable if Magnetic field remains constant. Now that is the problem I am facing. The magnetic field is not constant . – Priyanshu Mar 8 at 6:09
• If it's any help, there's such a thing as an earth inductor compass. It uses a spinning coil in the earth's magnetic field. The brushes can be turned, making a very sensitive compass. – Mike Dunlavey Mar 8 at 19:31