Question

A pair of point charges,$q=+4.00\mu C$ and $q^{{}^{\prime }}=-1.50\mu C$,are moving in a reference frame as shown in figure.At this instant, the magnitude of the magnetic field produced at the origin is 164$\times {10}^{-x}$. Find the value of x. (Take $v=2.00\times {10}^{5}m/s$ and $v^{{}^{\prime }}=8.00\times {10}^{5}m/s$.)

Answer 1

Applying, $\overrightarrow{B}=\frac{{\mu }_o}{4\pi }\frac{q}{r^3}(\overrightarrow{v}\times \overrightarrow{r})$ for both charges.Net magnetic field at centre is:
$\overrightarrow{B}=\frac{\left({10}^{-7}\right)(4\times {10}^{-6})}{{\left(0.3\right)}^3}\left[\right(2\times {10}^5\hat{i})\times (-0.3\left)\hat{j}\right)]+\frac{\left({10}^{-7}\right)(-1.5\times {10}^{-6})}{{\left(0.4\right)}^3}\left[\right(8\times {10}^5\hat{i})\times (-0.4\left)\hat{j}\right)]$

$=(-8.9\times {10}^{-7}\hat{k}-7.5\times {10}^{-8}\hat{k})$
$=(-1.64\times {10}^{-6})$