Question

In the figure shown, A is a fixed charged. B (of mass m) is given a velocity $v$ as shown in figure. At this moment the radius of curvature of the resultant path of B is :

• A. $\frac{8\pi {\epsilon }_0{r}^{2}m{v}^2}{\sqrt{3}{q}^2}$
• B. $\frac{4\pi {ϵ}_0{r}^{2}m{v}^2}{q^2}$
• C. $\frac{3\pi {\epsilon }_0{r}^{2}m{v}^2}{q^2}$
• D. $r$

Answer 1

Answer: (B)

$F=\frac{k{q}^2}{r^2}=\frac{m{v}^2}{R_c}$

$\Rightarrow R_c=\frac{m{v}^2}{F}=\frac{m{v}^2}{\frac{k{q}^2}{r^2}}=\frac{4\pi {\epsilon }_0{r}^{2}m{v}^2}{q^2}$