Two charges q and –3q are placed fixed on x-axis separated by distance ‘d’. Where a third charge 2q should be placed such that it will not experience any force?

The charge +2q should be placed to the right of +q charge because if it is placed in between +q and -3q charge both will apply the force in same direction and should be placed close to +q charge because the magnitude is less as compare to +3q charge ,so distance should be less too.

Let suppose it is placed at distance x from +q as shown in fig 1.23 a.

Using Coulomb’s law,

The force on +2q Charge due to +q charge is = k

And the force on +2q Charge due to -3q charge is = k

Where K is Coulombs constant

i.e K= k = 9×10⁹ N �m² �C⁻²

So the net force on +2q charge will be

And according to question net force should be equal to zero.

∴

⇒

⇒ =

Simplifying it we will get the two value of x

⇒ =

Here,

Now,

x=

=

=

=

On rationalising we get,

=

=

=

On solving we get

Now we will exclude the negative value as we have discussed the +2q charge can’t be placed in between.

As d - will lie in between the charges.So we have to neglect the –ive value,

So