Motional Emf In A Rotating Rod — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Motional EMF in a Rotating Rod Applies to a straight conducting rod of length L rotating with angular velocity ω about an axis passing through one of its ends, in a uniform magnetic field B perpendicular to the plane of rotation. Consider a small element of length dx at a distance x from the axis of rotation. The linear velocity of this element is v = ωx. The motional EMF induced in this small element is dε = B(v)dx = B(ωx)dx. Integrate dε from x = 0 to x = L to get the total EMF. Total ε = ∫(Bωx)dx from 0 to L = Bω[x²/2] from 0 to L. Result: ε = (1/2)BωL². The magnetic field B must be uniform and perpendicular to the plane of rotation. The rod acts as a rigid body. The rotation axis must pass through one end of the rod (if rotating about the center, potential difference across ends is zero). Frequency given in RPM must be converted to rad/s (ω = 2πf). Assuming EMF is generated when the axis of rotation is parallel to the magnetic field lines (No flux is cut). Confusing the potential difference across the ends (ε) with the potential difference between the center and an end when rotated about the center. Forgetting the factor of 1/2, erroneously using BvL where v is the tip velocity. Neglecting to convert frequency from Hz or RPM to angular velocity (rad/s).