First slide

Motional EMF

Question

A uniform magnetic field exists in the region given by $\vec{B} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k}$ . A rod of length 5 m placed along Y-axis is moved along X-axis with constant speed $1 {ms}^{- 1}$ . Then induced e.m.f in the rod is

Moderate

A

Zero
B

25 V
C

5 V
D

10 V

Solution

$l = 5 j$
$V = 1 i$
$e = B (l \times V)$
$= B |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & 5 & 0 \\ 1 & 0 & 0 \end{matrix}|$
$= B (0 - 5 \hat{K})$
$(3 \hat{i} + 4 \hat{j} + 5 \hat{k}) . (- 5 \hat{k})$
$= 25 V$
Conceptual approach:-
As the rod is placed along Y axis and moving in x direction, the magnetic field has to be perpendicular to both $\vec{l} and \vec{v}$ in order to develop motional emf. Hence the z component of the magnetic field should be taken.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App