Question

A straight conductor of length $0.4m$ is moving with a speed of $7m{s}^{-1}$ perpendicular to the magnetic field of intensity of $0.9Wb{m}^{-2}$ . The induced emf across the conductor will be

• A. $7.25V$
• B. $5.52V$
• C. $1.25V$
• D. $2.52V$

Answer 1

Answer: (D)

If a rod of length $l$ is moved with velocity $\overrightarrow{v}$ at an angle $\theta$ to the length of the rod in a filed $\overrightarrow{B}$ which is perpendicular to the plane of motion, the flux linked with the area generated by the motion of rod in time t.
$\varphi =Bl\left(vsin\theta \right)t$
So, $e=\frac{d\varphi }{dt}=Bvlsin\theta$
This will be maximum when


$sin\theta =max=1$
i.e., the rod is moving perpendicular to its length and then
${\left(e\right)}_{max}=Bvl$
$\therefore e=0.9\times 7\times 0.4=2.52V$