Two charges $1 * 10^{-6} C$ and $-4 * 10^{-6} C$ are separated by a distance of $2\;m$. Determine the position of the null point.

Given, (need figure)

First charge $(q_1) = 1 * 10^{-6}\;C$

Second charge $(q_2) = -4 * 10^{-6}\;C$

Distance $(r) = 2\;m$

Let C be the null point at a distance $x$ from the charge.

At null point, Force due to charge $(q_1)$ = Force due to charge ($-q_2$)

or, $\frac{1}{4\pi\epsilon_0}\frac{q_1 \;* \;q}{x^2} = \frac{1}{4\pi\epsilon_0}\frac{q_2 \; * \;q}{(r\;+\;x)^2}$

or, $\frac{q_1}{x^2} = \frac{q_2}{(r\;+\;x)^2}$

or, $\frac{(r\;+\;x)^2}{x^2} = \frac{4 \;* \;10^{-6}}{1 \;*\; 10^{-6}}$

or, $(\frac{r \;+\;x}{x})^2$$= 4$

or, $(\frac{r \;+\;x}{x})$$= 2$

or, $(\frac{2 \;+\;x}{x})$$= 2$                             [∵ r = 2 m]

⇒ $x = 2\;m$

∴ Position of the null point from the $q_1$ charge is $2\;m$

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