Question

A conducting rod of $1\text{m}$ length is rotating with a frequency of $50\text{rev/s}$ inside the uniform magnetic field of $6.28\text{mT}$. The magnetic field is perpendicular to the plane of rotation.

If the conducting rod is rotating about an axis passing through one of its end, then find the emf induced between the ends of the rod.

​​​​​​​$[$1 Mark$]$

• A. $1\text{V}$
• B. $2\text{V}$
• C. $0.5\text{V}$
• D. Zero

Answer 1

The correct option is A $1\text{V}$

A rotational emf will be induced when the rod is rotating in a magnetic field perpendicular to the plane of rotation.

Rotational EMF,

$\epsilon =\frac{B\omega l^2}{2}$

Where,

$B=$ Magnitude of magnetic field
$\omega =$ Angular frequency of rotation
$l=$ length of the rod

$\Rightarrow \epsilon =\frac{(6.28\times {10}^{-3})\cdot (2\pi \times 50)\cdot \left(1{)}^2\right)}{2}$

$\Rightarrow \epsilon \approx 1\text{V}$