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Unreasonable Results An inventor wants to generate $120-$ V power by moving a 1.00 -m-long wire perpendicular to the Earth's $5.00 \times 10^{-5} \mathrm{T}$ field. (a) Find the speed with which the wire must move. (b) What is unreasonable about this result? (c) Which assumption is responsible?

Part (a): $2.40 \times 10^{6} \mathrm{m} / \mathrm{s}$Part (b): The speed is so high to be applicable.Part (c): The Earth's magnetic field is so weak for generating this amount of energy by just 1.0 -m wire.

Physics 102 Electricity and Magnetism

Chapter 22

Magnetism

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Electromagnetic Induction

Inductance

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

McMaster University

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So we went to generate 120 Well, power because the one met meter long wire Ah, which is moving in a perpendicular magnetic failed created by the heirs and Earth's magnetic field is five ah, 10 mine 10 minus five. That's weak. So there should be 10 minus five day slim. And what would be the speed? What should be the speed off a friend of this y ear? In order to get these amounts off well, teach acres its ends. So as we men there, you generated by this motion is pv el. This is the famous formal, um, And from here we can find we can find, Ah, the velocity which is necessary to generate these amounts of world teach. But legis ta derived these Ah, this formula. So we have a wire which is moving with the velocity and we have a perpendicular magnetic field. And let's consider positively charge a positively charged particle inside this wire which is free to move. And while it's moving with the wire with a velocity Oh, we there would be a arised a force from the magnetic field which would be directed upwards and same would be true for other positively for every positively charged particle inside this wire. So after some time there will be some prostitute charged charge I couldn't accumulated at the upper end and and negative charge accumulated at the lower end. And this would create an electric field or world Ege and the distribution would stop when the electric field created uh would compensate the magnetic force. So electric force is Q E. Let's consider some arbitrary, arbitrary charge inside the Y you're after some time so Kui should be Q B B for forced from the magnetic field and the equilibrium electric field would be the B and the world teach would be e multiplied by distance by the length of the wire e l and we get Devi l. This was just a close with and from here we can find we can find the velocity. So this is the well, our city. This is not equal. So velocity is you're he waited by the hour and de ces two point for 10 in the six power And the next question is if the's is reasonable, if we can do some such experiment and this is not possible because this speed necessary to gain these, uh, Emma's. The voltage is too high for reality wound. What would be the reasonable, reasonable expectation and wildly magnetic field is so weak? Uh, we can generate these world ege. So we should expect, like Lacewell t took voltage to be generated because we have a limitation on speed. So let's say 0.1. Well, let's expect 0.1 world. It means that we would need 10,000 times place speed to generate the 0.1 world. And this is about around 200 meters per second. And this is kind off reasonable toe. Move a wire with the 200 meetings for a second. Well, is it?

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