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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