91Ó°ÊÓ

Consider the given figure

Q₁=4e

Q₂=1e

Where e=charge

The position at which $\stackrel{→}{E}=\stackrel{→}{0}\text{is}\left|\stackrel{→}{F_1}\right|=\left|\stackrel{→}{F_2}\right|……\left(1\right)$

Here,

$\underset{F1}{→=}$Columbic force between the charge Q1 & test charge Q

localid="1648533539776" $\underset{F1}{→}=$Columbic force between the charge Q2 & test charge Q

$\left|\stackrel{→}{F}\right|=\text{Columbic force}=\frac{q_1{q}_2}{4\mathrm{Ï€}{\mathrm{Î\mu }}_0{d}^2}……\left(2\right)$

Where, q₁&q₂ are two charges separated by distance d.

It is to be noted that, choosing the position of the test charge should satisfy the condition that $\underset{F1}{→}$$\&$$\underset{F2}{→}$should be in opposite direction.

Now substituting the given data in eqns (1) & (2)

$$\begin{gathered} ⇒\left|\frac{\left(4e\right)\left(Q\right)}{4\mathrm{Ï€}{\mathrm{Î\mu }}_0{D}^2}\right|=\left|\frac{\left(1e\right)\left(Q\right)}{4\mathrm{Ï€}{\mathrm{Î\mu }}_0{r}^2}\right| \\ ⇒2r=D……\left(3\right) \end{gathered}$$

By considering eqn(3), for the present scenario, the final figure pertinent to the position at which $\underset{E}{→}$$=$$\underset{0}{→}$is as shown below

Consider the given figure

Q₁=4e

Q₂=1e

Where e=charge

The position at which $\stackrel{→}{E}=\stackrel{→}{0}\text{is}\left|\stackrel{→}{F_1}\right|=\left|\stackrel{→}{F_2}\right|……\left(1\right)$

It is to be noted that, choosing the position of the test charge should satisfy the condition that $\underset{F1}{→}$$\&$$\underset{F2}{→}$should be in opposite direction.

$\left|\stackrel{→}{F}\right|=\text{Columbic force}=\frac{q_1{q}_2}{4\mathrm{Ï€}{\mathrm{Î\mu }}_0{d}^2}……\left(2\right)$

Now substituting the given data in eqns (1) $ (2)

$$\begin{gathered} ⇒\left|\frac{\left(4e\right)\left(Q\right)}{4\mathrm{Ï€}{\mathrm{Î\mu }}_0{D}^2}\right|=\left|\frac{(-1e)\left(Q\right)}{4\mathrm{Ï€}{\mathrm{Î\mu }}_0{r}^2}\right| \\ ⇒2r=D……\left(3\right) \end{gathered}$$

By considering eqn(3), for the present scenario, to the final figure pertinent to the position at which $\underset{E}{→}$$=$$\underset{0}{→}$is as shown below