Question

Uniform magnetic field exists in region given by B=3i+4j+5k . A rod of length 5 m is placed along y - axis is moved along x axis with constant speed 1 m/sec. Then the magnitude of induced e.m.f in the rod is :

• A. zero
• B. 25 volt
• C. 20 volt
• D. 15 volt

Answer 1

Answer: (B)

Given: $\vec{B}=3\hat{i}+4\hat{j}+5\hat{k}$
Length of rod $\vec{l}=5\hat{j}$
Velocity of rod $\vec{v}=1\hat{i}$
Induced emf is given by $E=(\vec{v}\times \vec{B})\cdot \vec{l}$
$\therefore E=(1\hat{i}\times (3\hat{i}+4\hat{j}+5\hat{k})]\cdot (5\hat{j})$
Or $E=(4\hat{k}-5\hat{j})\cdot (5\hat{j})=-25$ volts
$\overrightarrow{|}E|=25$ volts