Question

A uniform magnetic field exists in a region given by $\vec{B}=3\hat{i}+4\hat{j}+5\hat{k}T$. A rod of length $5m$ is placed along the $y$-axis and it is moved along the $x$-axis with constant speed $1m{s}^{-1}$. Then induced e.m.f. in the rod will be

• A. zero
• B. $25V$
• C. $20V$
• D. $15V$

Answer 1

Answer: (B)

We know that
Magnetic field vector $\vec{B}=3\hat{i}+4\hat{j}+5\hat{k}$
length of rod $\vec{L}=5\hat{j}$
velocity vector $\vec{v}=1\hat{i}$
Induced emf is given as
$E=\vec{L}\cdot (\vec{v}\times \vec{B})$
$E=(5\hat{j})\cdot [(1\hat{i})\times (3\hat{i}+4\hat{j}+5\hat{k})]$
$E=(5\hat{j})\cdot (-5\hat{j}+4\hat{k})$
$E=-25V$