# A uniform magnetic field exists in a region given by B = 3i ̂+ 4j ̂+ 5k ̂. A rod of length 5m along y-axis moves with …..

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) 25V

(c) 20V

(d) 15V

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