Question

A uniform magnetic field, $\overrightarrow{B}=(3\hat{i}+4\hat{j}+5\hat{k})\text{T}$, exists in a region. A rod of length $5\text{m}$, placed along $y-$axis, is moved along $x-$axis with constant speed of $1{\text{ms}}^{-1}$. The magnitude of induced emf in the rod is -

• A. Zero
• B. $25\text{V}$
• C. $5\text{V}$
• D. $10\text{V}$

Answer 1

The correct option is B $25\text{V}$

The rod is placed along the $y-$axis, therefore,
$\overrightarrow{l}=\left(5\hat{j}\right)\text{m}$

The rod is moving along the $x-$axis, therefore,
$\overrightarrow{v}=\left(1\hat{i}\right)\text{m/s}$

The induced emf is,

$E=(\overrightarrow{v}\times \overrightarrow{B})\cdot \overrightarrow{l}$

$=\left[\right(1\hat{i})\times (3\hat{i}+4\hat{j}+5\hat{k}\left)\right]\cdot \left(5\hat{j}\right)$

$=[4\hat{k}-5\hat{j}]\cdot \left(5\hat{j}\right)$

$\therefore E=-25\text{V}$

Hence, option $\left(B\right)$ is the correct answer.