Question

A conducting rod of length L lies along the y–axis with one end at origin and the other end at (0, L, 0). There is a magnetic field B = B₀y\(\hat{k}\) in that region. If the rod moves with a velocity V = V₀\(\hat{i}\), the e.m.f induced between the ends of the rod will be

(1) \(\frac{B_0V_0L}{2}\)

(2) \(\frac{B_0V_0L^2}{2}\)

(3) B₀V₀ Ld

(4) \(\frac{B_0V_0L^2}{4}\)

Answer 1

 (2) \(\frac{B_0V_0L^2}{2}\)

The induced emf, across a small element dy of the rod is

∴ The induced emf across the rod of length L will be