Question

A long straight rod $\text{AB}$ of length $2\text{m}$ moves in a uniform magnetic field of magnitude $B=0.5\text{T}$ with a velocity of $10{\text{ms}}^{-1}$ as shown in the figure. Find the emf induced in the rod.

• A. $5\text{V}$
• B. $6\text{V}$
• C. $10\text{V}$
• D. $1.5\text{V}$

Answer 1

The correct option is B $6\text{V}$

Emf will be generated in the rod due to the component of the velocity which is perpendicular to its length, as well as the field $B.$

$\therefore E=Bl\left(v\sin \theta \right)$

$E=0.5\times 2\times (10\times \sin {37}^{\circ })$

$\therefore E=1\times 10\times \frac{3}{5}=6\text{V}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\text{(B)}$ is the correct answer.

Why this question ? Key concept : While applying the formula for motional emf, consider the component of velocity which is perpendicular to the length of the rod as well as to the magnetic field.