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  4. A charge particle is moving in a uniform magnetic field (2 hat i +3 hat j ) T. If it has an acceleration of (α hati-4 hatj) m / s 2, then the value of α will be

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Q. A charge particle is moving in a uniform magnetic field $(2 \hat{ i }+3 \hat{ j }) T$. If it has an acceleration of $(\alpha \hat{i}-4 \hat{j}) m / s ^2$, then the value of $\alpha$ will be

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Solution:

As $ \vec{F}=q(\vec{v} \times \vec{B}) $
$ \vec{a}=\frac{q}{m}(\vec{v} \times \vec{B})$
So, $\vec{a} \& \vec{B}$ are $\perp$ to each other
Hence, $\vec{a} \cdot \vec{B}=0$
$ (\alpha \hat{i}-4 \hat{j}) \cdot(2 \hat{i}+3 \hat{j})=0$
$ \alpha(2)+(-4)(3)=0 $
$\alpha=\frac{12}{2} \Rightarrow \alpha=6$