The magnetic force acting on a charged particle of charge $-2\ \mu$...

Question

The magnetic force acting on a charged particle of charge $-2\ \mu$C in a magnetic field of 2 T acting in y-direction, when the particle velocity is $(2\hat{i} + 3\hat{j}) 	imes 10^6$ m/s, is

Accepted Answer

$q = -2 	imes 10^{-6}$ C, $\vec{B} = 2\hat{j}$ T, $\vec{v} = (2\hat{i} + 3\hat{j}) 	imes 10^6$ m/s

$$\vec{v} 	imes \vec{B} = (2\hat{i} + 3\hat{j}) 	imes 10^6 	imes 2\hat{j} = 10^6[(2\hat{i} 	imes 2\hat{j}) + (3\hat{j} 	imes 2\hat{j})]$$
$$= 10^6[4\hat{k} + 0] = 4 	imes 10^6\hat{k}$$

$$\vec{F} = q(\vec{v} 	imes \vec{B}) = -2 	imes 10^{-6} 	imes 4 	imes 10^6\hat{k} = -8\hat{k} 	ext{ N}$$

Force $= 8$ N along $-z$ direction.

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