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The charged particle moving in a uniform magnetic field of $$(3\hat{i} + 2\hat{j})$$ T has an acceleration $$\left(4\hat{i} - \frac{x}{2}\hat{j}\right)$$ m/s$$^2$$. The value of $$x$$ is
Correct Answer: 12
In a magnetic field, acceleration is perpendicular to the magnetic field:
a ⟂ B ⇒ a · B = 0
Given:
$$B=(3i+2j)$$
$$a=(4i−\frac{x}{2}j)$$
dot product:
$$(4)(3)+\left(\frac{−x}{2}\right)(2)=0$$
12 − x = 0
x = 12
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