diamagfarady__1.png

The electron moves in a circular path of radius $r$ under the influence of the inward force
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Now we add magnetic field in the direction out of the page. The inward force increases to
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so either $r$ or $v$ must change. previously we aserted that $v$ changes, and thus
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so
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We are to show that the induced electric field produces exactly this change in $v.$ With positive direction around the circle defined to be clockwise, the induced electric field is given by
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So
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and the force tangent to the electron's path that changes its speed is
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Integrating, we get
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as required.

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