A horizontal metallic rod of mass $'m'$ and length $'l'$ is supported by two vertical identical springs of spring of spring constant $'K'$ each and natural length $l_0.$ A current $'i'$ is flowing in the rod in the direction shown. If the rod is in equilibrium then the length of each spring in this state is :-
Diffcult
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The force on the rod due to magnetic field and gravity is
$ilB - mg$ (upwards)
Hence the extension in the springs is $\frac{{ilB - mg}}{{2k}}$ (Note that effective spring constant is $2k$)
Therefore the length of the spring is $\ell_{0}+$ $\frac{{ilB - mg}}{{2k}}$
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