Q. A conductor AB of length *l* moves in x-y plane with velocity $ \displaystyle \vec{v} = v_0(\hat{i}-\hat{j})$ . A magnetic field $\displaystyle \vec{B} = B_0(\hat{i}+\hat{j})$ exists in the region. The induced emf is

(a) zero

(b) 2B_{0}*lv*_{0}

(c) B_{0}*lv*_{0}

(d) √2 B_{0}*lv*_{0}

Ans: (a)

Sol: Since velocity & magnetic field are in X-Y Plane , hence their vector Product is Perpendicular to X-Y plane .

Since $\displaystyle (\vec{v}\times \vec{B})$ is Perpendicular to $\displaystyle \vec{l}$

$ \displaystyle \vec{l}.(\vec{v}\times \vec{B}) = 0 $

Induced emf , $\displaystyle E = \vec{l}.(\vec{v}\times \vec{B})$

E = 0