Answer

Verified

87.3k+ views

**Hint**For 2 charges separated by some distance, there will be separate forces on any other point. Let's say that there is a charge between the two charges on the line joining them. The direction of forces will be opposite due to these charges. So this third charge is kept at such a position that the two forces cancel out. We will have to find this equivalence point

**Complete step by step solution**

Let the equivalence point be at a distance of x from the first charge. The distance of that point from the second charge will be 1-x meters. Place a charge Q at this distance to find the equivalence point. Now we need to calculate the force exerted by the 1st charge on charge on the charge Q.

\[

F\, = \,\dfrac{{kqQ}}{{{r^2}}} \\

F\, = \,9 \times {10^9}\dfrac{{1x{{10}^{ - 9}}Q}}{{{x^2}}} \\

\]

Now the force generated by the 2nd charge on charge Q is equal to ;

\[

F\, = \,\dfrac{{kqQ}}{{{r^2}}} \\

F\, = \,9 \times {10^9}\dfrac{{9x{{10}^{ - 9}}Q}}{{{{(1 - x)}^2}}} \\

\]

Now these 2 force should balance each other out. therefore, equating the 2 forces we get:

\[9 \times {10^9}\dfrac{{9 \times {{10}^{ - 9}}Q}}{{{{(1 - x)}^2}}}\, = \,9 \times {10^9}\dfrac{{{{10}^{ - 9}}Q}}{{{x^2}}}\]

\[

\dfrac{9}{{{{(1 - x)}^2}}}\, = \,\dfrac{1}{{{x^2}}} \\

9{x^2} = {(1 - x)^2} \\

\pm 3x\, = \,1 - x \\

\]

This gives us 2 values of x

\[

3x\, = \,1 - x \\

x = 0.25 \\

\]

And

\[

- 3x\, = \,1 - x \\

- 2x\, = \,1 \\

x\, = \, - 0.5 \\

\]

Here negative signs mean away from the 2nd charge

If the net force is 0 at 0.25 from 1st charge, it will also be 0 at 0.75m from the second charge.

**Therefore the option with the correct answer is option C**

**Note**We didn’t take the 2nd value of x because the charges given are like charges. So if a charge Q is placed at away from the 2nd charge, it will be attracted by one of them and repelled by the other, which will result in a net force.

Note the sign of the force. We need the forces to cancel out.

Recently Updated Pages

Name the scale on which the destructive energy of an class 11 physics JEE_Main

Write an article on the need and importance of sports class 10 english JEE_Main

Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main

Choose the one which best expresses the meaning of class 9 english JEE_Main

What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main

A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main

Other Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

A lens forms a sharp image on a screen On inserting class 12 physics JEE_MAIN

Which of the following facts regarding bond order is class 11 chemistry JEE_Main

Velocity of car at t 0 is u moves with a constant acceleration class 11 physics JEE_Main

Find the number of nitrates which gives NO2gas on heating class 12 chemistry JEE_Main

If temperature of sun is decreased by 1 then the value class 11 physics JEE_Main