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Electricity and Magnetism Level 5

An arrangement of smooth pair of long conducting rails which are non resisting are joined to a charged capacitor. The rails are connected by a rod of mass \(M\), length \(L\), and Resistance \(R\). A vertical Magnetic Field \(B\) is established in the region. The rod starts moving due to the influence of the Magnetic Field.

What should be the mass of the rod \(M\) (in mg) so that its Kinetic Energy in steady state is maximum?

Details and Assumptions:
\(\bullet L=1m\)
\(\bullet B=2T\)
\(\bullet C=1\mu F\)
\(\bullet R=1\)ohm
\(\bullet\) The Rod is initially at rest
\(\bullet\) The Magnetic Field is constant and uniform in nature


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