Question

A particle is moving with velocity $\overrightarrow{v}=\hat{i}+3\hat{j}$ and it produces an electric field at that point equal to $2\hat{k}$, find the magnetic field at that point (all quantities are in SI units)

• A. $(6\hat{i}-2\hat{j}){\mu }_0{\epsilon }_0$
• B. $(6\hat{i}+2\hat{j}){\mu }_0{\epsilon }_0$
• C. zero
• D. cannot be determined from the given data

Answer 1

The correct option is A $(6\hat{i}-2\hat{j}){\mu }_0{\epsilon }_0$

$\overrightarrow{E}=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r^2}\hat{r}=2\hat{k},\hat{r}=\hat{k}$

$\overrightarrow{B}=\frac{{\mu }_0}{2\pi }\frac{q\overrightarrow{v}\hat{r}}{r^2}={\mu }_0{\epsilon }_0\left[\frac{q}{4\pi {\epsilon }_0{r}^2}\right](\hat{i}+3\hat{j})\times \hat{k}$

$={\mu }_0{\epsilon }_{0}2[-\hat{j}+3\hat{i}]=(6\hat{i}-2\hat{j}){\mu }_0{\epsilon }_0$