A conducting rod of length l is hinged at point O. It is free to rotate in a vertical plane. There exists a uniform magnetic field B in horizontal direction. The rod is released from the position. What is the potential difference between the two ends of the rod is proportional to?

Published On: July 17, 2022

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The gravitational potential decreases to increase the kinetic energy of the rod. The equation can be written as,

mg 1/2sinθ = 1/2Iω2 = 1/2(ml2/3)ω2

⟹ ω=√3g/lsinθ

Hence the magnetic field and the direction of velocity of rods is perpendicular.

Total potential difference developed across the ends =

B(xω)dx

=Bl2/2√ 3g/lsinθ ∝ l3/2√sinθ.