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