Question Video: Determining Potential Difference Induced across an Aircraft’s Wings | Nagwa Question Video: Determining Potential Difference Induced across an Aircraft’s Wings | Nagwa

# Question Video: Determining Potential Difference Induced across an Aircraft’s Wings Physics • Third Year of Secondary School

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A small aircraft flies at 150 m/s through a region where the strength of Earth’s magnetic field perpendicular to its wings is 35 𝜇T. The wingspan of the aircraft is 12 m. What potential difference is induced across the aircraft’s wingtips?

03:17

### Video Transcript

A small aircraft flies at 150 meters per second through a region where the strength of Earth’s magnetic field perpendicular to its wings is 35 microteslas. The wingspan of the aircraft is 12 meters. What potential difference is induced across the aircraft’s wingtips?

If we picture this plane from an aerial perspective, we can imagine it flying to the right with a speed we’ll call 𝑣. The wingspan of the aircraft, what we’ll call 𝑙, is 12 meters. And we know that as this plane flies along, it moves through Earth’s magnetic field. Specifically, that field is perpendicular to the wings of the plane. That could mean that the magnetic field points out of the screen at us or into the screen away from us. We actually don’t need to decide which of these two it is. In either case, whichever way the magnetic field points, it’s perpendicular to the plane’s velocity 𝑣. Since the magnetic field, though, does only point in one of these two directions, we can pick one at random and then move on to answering our question of what the potential difference induced across the aircraft’s wingtips is.

The idea here is that the wings of the aircraft are made of some metal. Therefore, they are conductors with mobile electric charge. Given a magnetic field we’ll call 𝐵 that points into the screen, we would expect positive electrical charge to accumulate at this end of the aircraft’s wingspan and negative charge down here. However, it’s not the polarity of charge across the wingspan that we’re interested in, but rather the total potential difference across that wingspan. For a straight conductor of length 𝑙 moving at a speed 𝑣 through a magnetic field of strength 𝐵, the potential difference, also called the emf, induced across that conductor is 𝑙 times 𝑣 times 𝐵 times the sin of this angle called 𝜃. 𝜃, it turns out, is the angle between the velocity vector and the magnetic field vector involved in the scenario.

We can see from the fact that this equation uses the sin of 𝜃 that when 𝜃 is 90 degrees, the emf, or potential difference induced, will be a maximum value. This is just what happens in our particular scenario, with our plane moving perpendicularly to the magnetic field. The potential difference induced across the wingtips is equal to 𝑙 times 𝑣 times 𝐵 times the sin of 90 degrees or, since the sin of 90 degrees is one, 𝑙 times 𝑣 times 𝐵. We’re given values for all three of these variables.

But notice that our magnetic field has units of microtesla. Before we calculate the potential difference, we’d like to change this over into units simply of teslas. The conversion between these units is that one million microteslas is equal to one tesla. To convert microteslas to teslas then, we would divide by one million. Perhaps the simplest way to solve for the equivalent value of magnetic field in teslas is to multiply by 10 to the negative six. That means we have thirty-five one one millionth of a tesla.

Our units are now all in order, and we’re ready to calculate the potential difference. Rounding to two significant figures and note that leading zeros are never significant in a number, the potential difference we calculate is 0.063 volts. That’s the potential difference induced across the aircraft’s wingtips. Notice that this potential difference is much smaller than even the typical potential difference supplied by a standard cell or battery. In other words, it would be difficult to make the potential difference generated by this aircraft’s motion through a magnetic field useful. To make it so, we might need to significantly increase the aircraft speed or significantly increase its wingspan.

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