Q. A uniform magnetic field exists in a region given by Induced emf , $\displaystyle \vec{B} = 3 \hat{i} + 4\hat{j} + 5 \hat{k} $ . A rod of length 5m along y-axis moves with a constant speed of 1 ms^{-1} along x axis. Then the induced emf in the rod will be

(a) 0

(b) 25 V

(c) 20 V

(d) 15 V

Ans: (b)

Sol: Induced emf $\displaystyle E = \vec{l}.[\vec{v}\times \vec{B}]$

$ \displaystyle E = 5 \hat{j}.[1 \hat{i} \times (3 \hat{i} + 4\hat{j} + 5 \hat{k})]$

$ \displaystyle E = 5 \hat{j}.[4\hat{k} – 5 \hat{j}]$

E = – 25

E = 25 volt