Question

Two conducting wires are joined together and are moving in a magnetic field perpendicular to the plane of the wires, as shown in the figure. Find the induced emf developed across the ends $O$ and $Q$.

• A. $10\text{V}$
• B. $50\text{V}$
• C. $40\text{V}$
• D. $32\text{V}$

Answer 1

The correct option is C $40\text{V}$


The effective length of the wire between points $O$ and $Q$ is,

$l=OQ=\sqrt{1^2+2^2}=\sqrt{5}\text{m}$

Now, EMF induced across the ends $O$ and $Q$ is,

$E=\frac{B\omega l^2}{2}=\frac{0.8\times 20\times (\sqrt{5}{)}^2}{2}=40\text{V}$

Hence, option $\left(D\right)$ is the correct answer.