Question

Two electrons move parallel to each other with equal speed $V$, the ratio of magnetic & electric force between them is :

• A. $\frac{V}{C}$
• B. $(\frac{V}{C}{)}^{-1}$
• C. $(\frac{V}{C}{)}^2$
• D. $(\frac{V}{C}{)}^{-2}$

Answer 1

Answer: (C)

$(\frac{V}{C}{)}^2$

Electric force$\left(F_e\right)=\frac{q_1{q}_2}{4\pi ϵr^2}=\frac{e^2}{4\pi {ϵ}_0{r}^2}$

magnetic field B $=\frac{{\mu }_0}{4\pi }\frac{q(\overrightarrow{v}\times \overrightarrow{r})}{r^2}$
Magnetic force $F_m=q(\underset{V}{\to }\times \underset{B}{\to })=q\frac{{\mu }_0}{4\pi }q\frac{v_1{v}_2}{r^2}$
$=\frac{{\mu }_0}{4\pi }\frac{e^1{v}^2}{r^2}$
$\frac{F_m}{F_e}={\mu }_0{\epsilon }_0{V}^2$
but ${\mu }_0{\epsilon }_0=\frac{1}{c^2}\Rightarrow \frac{F_m}{F_e}=\frac{V^2}{C^2}$