# Induced Voltage in an unclosed loop

#### AlejandroDes

I read the following problem on a text book:

A airplane flies at a constant speed of 680m/s perpendiculary to earth's magnetic field (of 5x10^-5 T). The wingspan of the airplane is 9.8m. What is the induced voltage?
The answer the book gives is: E = BLv = 0.4066V

But I've been wondering if this is true. There isn't and enclosed loop. How can a simple wire moving on a magnetic field induce voltage on its terminals?

http://www.physics.sjsu.edu/becker/physics51/30_25_Lenz%27s_law_(Exercise_30-16).JPG

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#### Henryk

Gold Member
Actually, when I plugged the numbers, I got 0.3332 V. But yes, there is a voltage induced across the wings. If the wingtips were touching two parallel and stationary rails, you could measure the voltage between the rails ( or power a light bulb)

#### Chandra Prayaga

Science Advisor
I read the following problem on a text book:

A airplane flies at a constant speed of 680m/s perpendiculary to earth's magnetic field (of 5x10^-5 T). The wingspan of the airplane is 9.8m. What is the induced voltage?
The answer the book gives is: E = BLv = 0.4066V

But I've been wondering if this is true. There isn't and enclosed loop. How can a simple wire moving on a magnetic field induce voltage on its terminals?

http://www.physics.sjsu.edu/becker/physics51/30_25_Lenz%27s_law_(Exercise_30-16).JPG
Apart from the numbers, the physical result is quite correct. You don't have to close the loop to get a voltage. Because of the velocity of the airplane, electrons in the wings have a magnetic force acting on them, pushing them toward the point a in your picture. This results in accumulation of electrons near point a, leaving behind an equal positive charge near point b. This separation of charges results in a voltage, with b at a higher, and a at a lower voltage. So this phenomenon is due to a magnetic force, and not due to induction.

#### Qwertywerty

Try understanding the reason for the induced voltage - when the rod moves through a magnetic field, a force acts on the electrons of the rod. This pushes them towards one side , developing an area containing excess of electrons, and at the same time a deficiency of them on the other.

This leads to an electric field, and consequently, a potential difference across the rod. Understand, if it was a closed loop, provided it was conducting, there would be , simply, a current flowing through the loop.

Hope this helps.

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