A metallic rod of length 'L' is rotated with an angular speed of ‘ω’ normal to a uniform magnetic field 'B' about an axis passing through one end of rod as shown in figure. The induced emf will be :

Question

G1 Physics · Accepted Answer

At distance x from the axis, speed v = ωx. The emf across element dx is dε = Bv dx = Bωx dx. Integrating from x = 0 to L: ε = ∫₀ᴸ Bωx dx = (1/2)BωL².