How close to get the same force back?

Two charges are moved from air into water (take its dielectric constant as 81). To feel the same force as they did in air, their separation must become:

Answer: r/9.

In water the force is divided by K = 81. Since the force goes as one over the distance squared, the separation must shrink by √81 = 9 to win that factor back.

\frac{q_{1} q_{2}}{4 π ε_{0} K r^{' 2}} = \frac{q_{1} q_{2}}{4 π ε_{0} r^{2}}

\Rightarrow r' = \frac{r}{\sqrt{K}} = \frac{r}{9}

The charges must be 9 times closer, at r/9. Dividing the distance by 81 forgets that the force depends on the square of the distance.

Original practice question · JEE Physics Decoded

What is Level 2?

One step past the obvious.

Every Level 2 starts from a quick question, Level 1, and changes one thing. Seeing what that change does is the skill JEE Main tests. Try it here, free and with no signup, then read the worked answer.

Practise more like this, free Continue practising All Level 2 questions

Free account · Students 15+ in India · Parent approval under 18

Get the Android app on Google Play → (opens in a new tab)

Keep going

Practise more like this, free.

Tests marked like the real exam, and a worked explanation for every question.

Start practising free

How close to get the same force back?

One step past the obvious.

More Level 2 questions

Practise more like this, free.