Question

A conducting rod $PQ$ of length $5\text{m}$ oriented as shown in the figure is moving with velocity $\left(2\hat{i}\right)\text{m/s}$, without rotation, in a uniform magnetic field of $(3\hat{j}+4\hat{k})\text{T}$. EMF induced in the rod is -

• A. $32\text{V}$
• B. $40\text{V}$
• C. $50\text{V}$
• D. None of these

Answer 1

The correct option is A $32\text{V}$


From the figure, we can see that, length vector for rod $PQ$,

$\overrightarrow{l}=(5\cos {53}^{\circ }\hat{i}+5\sin {53}^{\circ }\hat{j})\text{m/s}$

$\Rightarrow \overrightarrow{l}=(3\hat{i}+4\hat{j})\text{m/s}$

Now, the induced emf is given by,

$E=(\overrightarrow{v}\times \overrightarrow{B})\cdot \overrightarrow{l}$

Here,

$\overrightarrow{v}\times \overrightarrow{B}=\hat{i}(0-0)-\hat{j}(8-0)+\hat{k}(6-0)$

$\Rightarrow \overrightarrow{v}\times \overrightarrow{B}=6\hat{k}-8\hat{j}$

$\therefore E=(6\hat{k}-8\hat{j}).(3\hat{i}+4\hat{j})=-32\text{V}$

Considering magnitude only, $E=32\text{V}$

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