Question

A magnetic field of $8\hat{k}mT$ exerts a force of $(4.0\hat{i}+3.0\hat{j})\times {10}^{-10}N$ on a particle having a charging $5\times {10}^{-10}C$ and going in the $X-Y$ plane. Find the velocity of the particles.

Answer 1

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

$(4.0\hat{i}+3.0\hat{j})\times {10}^{-10}=5\times {10}^{-10}\times (x\hat{i}+y\hat{j}+z\hat{k})\times \left(8\hat{k}\right)$

$4.0\hat{i}+3.0\hat{j}=40[-\hat{j}x+\hat{i}y]$

$x=\frac{-3}{40}$

$y=\frac{4}{40}$

$\overrightarrow{V}=\frac{-3}{40}\hat{i}+\frac{4}{40}\hat{j}$