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Finding the equation of motion in a magnetic field

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The conductor bridge is giving an initial velocity V0 to the right. The circuit completed by this bridge has an increasing area as the bridge moves to the right which means an increasing magnetic flux. Thus we know from Faraday's law that a current is created in the circuit completed by this bridge proportional to its velocity. So if the bridge continues to move freely forever, we have an infinite source of energy through generation of current. How is this violation of energy conservation resolved?

Find the equation of motion of the bridge and show that it slows down to rest eventually.

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The equation of motion in a magnetic field is examined.

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Answer: The bridge does not continue to move freely. In fact it experiences a force opposing its motion and bringing it to rest.

This force is predicted by the equation for the lorentz force: F = Qv x B which in the case of our conductor equals;
F = -ILB
where "L" is the length of ...

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