Question

If a particle of charge q is moving with velocity v along the z - axis and the magnetic field B is acting along x - axis, use the expression $\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})$ to find the direction of the force F acting on it.

Answer 1

Given

v along x-axis $\overrightarrow{v}=v\hat{i}$

B along y-axis $\overrightarrow{B}=B\hat{j}$

$\overrightarrow{F}=q\overrightarrow{v}\times \overrightarrow{B}$

$\overrightarrow{F}=q\left(v\hat{i}\right)\times \left(B\hat{j}\right)$

$\overrightarrow{F}=qvB\hat{k}$

That is force is acting along z-axis.