Question

The force between two point charges q1 and q2 separated by a
distance ‘r’ in vacuum is ‘F’. At what distance between the
charges will the force become ‘8F

Answer 1

▶ Solution :

Given :

The force between two point charges q1 and q2 separated by a distance r in vaccum is F.

To Find :

At what distance between the charges will the force become 8F.

Concept :

▪ This question is completely based on concept of 'coulomb's law'.

▪ As per coulomb's law, Electrostatic force acts between two point charges is inversely proportional to the square of distance b/w them.

Mathematically,

$\boxed{\bf{\pink{F_e\propto \dfrac{1}{r^2}}}}$

Calculation :

$\implies\sf\:\dfrac{F}{F'}=\dfrac{{r'}^2}{r^2}\\ \\ \implies\sf\:\dfrac{F}{8F}=\dfrac{{r'}^2}{r^2}\\ \\ \implies\sf\:{r'}^2=\dfrac{r^2}{8}\\ \\ \implies\boxed{\bf{\orange{r'=\dfrac{r}{2\sqrt{2}}}}}$

Answer 2

Aɴꜱᴡᴇʀ

➠ $\large\green{\tt{r'=\frac{r}{2\sqrt{2}}}}$

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Gɪᴠᴇɴ

✏ The force between two point charges q1 and q2 separated by a distance r in vaccum is F

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ᴛᴏ ꜰɪɴᴅ

➤ At what distance between the charges will the force be 8F

_________________

Sᴛᴇᴘꜱ

☞ Concept used here,

✭ Its just based on the 'coulomb's law'.

✭ As per coulomb's law, Electrostatic force acts between two point charges is inversely proportional to the square of distance b/w them.

❍ Substituting the given values,

$\begin{lgathered}\dashrightarrow\tt\:\frac{F}{F'}=\frac{{r'}^2}{r^2}\\ \\ \dashrightarrow\tt\:\dfrac{F}{8F}=\frac{{r'}^2}{r^2}\\ \\ \dashrightarrow\tt\:{r'}^2=\frac{r^2}{8}\\ \\ \pink {\dashrightarrow{\tt{r'=\frac{r}{2\sqrt{2}}}}}\end{lgathered}$

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