A horizontal metallic rod of mass m and length l is supported by two vertical identical springs of spring constant, K each and natural length l 0 . A current i is flowing in the rod in the direction s

Question

A horizontal metallic rod of mass m and length l is supported by two vertical identical springs 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:

TestHub · Accepted Answer

The force on the rod due to the magnetic field and gravity is

$i l B - m g (u p w a r d s)$

Hence the extension in the springs is $\frac{i l B - m g}{2 k}$

$(N o t e$ that effective spring constant is 2k)

Therefore the length of the spring is $l_{0} + \frac{i l B - m g}{2 k}$

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