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I was reading this post: Method of calculating eddy currents of a conductor, is this correct? and I found it very interesting. They came to the conclusion that the power lost due to eddy currents was: $$𝑃=∫𝐸⋅𝐽𝑑𝑉=∫𝜎|𝐸|^2𝑑𝑉=𝜎𝐵^2𝑣^2𝑉$$ and that the braking force would be: $$𝐹=𝜎𝐵^2𝑣𝑉$$ I was wondering how energy loss due to the eddy currents can be represented, given the distance of the magnetic field that is traveled through. As you can't simply multiply the force by distance, due to the fact that force is dependent on velocity, how would you formulate energy? I'd imagine there would be integrals involved. I would appreciate any help!

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