Electrostatics Question 16
Question 16 - 2024 (31 Jan Shift 1)
Two charges $q$ and $3 q$ are separated by a distance ’ $r$ ’ in air. At a distance $x$ from charge $q$, the resultant electric field is zero. The value of $x$ is :
(1) $\frac{(1+\sqrt{3})}{r}$
(2) $\frac{r}{3(1+\sqrt{3})}$
(3) $\frac{r}{(1+\sqrt{3})}$
(4) $r(1+\sqrt{3})$
Show Answer
Answer: (3)
$\left(\vec{E} _{\text {net }}\right) _P=0$
$\frac{k q}{x^{2}}=\frac{k \cdot 3 q}{(r-x)^{2}}$
$(r-x)^{2}=3 x^{2}$
$r-x=\sqrt{3} x$
$x=\frac{r}{\sqrt{3}+1}$
