Question

Two charged particles are moving parallel to each other with velocity $v$ at a finite distance $d$. If these two particles have identical charges $q$ on them , then what is the ratio of magnetic force to electric force between two charges? ($c$ is speed of light$={\mu }_0{\epsilon }_0$)

• A. $\frac{c^2}{v^2}$
• B. $\frac{v^2}{c^2}$
• C. $\frac{v}{c}$
• D. $\frac{c}{v}$

Answer 1

The correct option is B $\frac{v^2}{c^2}$

Magnetic force between two moving charged particles is given by , $F_m=\frac{{\mu }_0}{4\pi }{q}^2\frac{v^2}{d^2}$

Electric force between two moving charged particles is given by, $F_e=\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{d^2}$

$\frac{F_m}{F_e}={\mu }_0{\epsilon }_0{v}^2=\frac{v^2}{c^2}$

Hence, option $\left(b\right)$ is the right answer.