IIT JEE Advanced 2011 Paper 1

The net force on one of the charges due to other charges is
F =

2kq2

a2

+

kq2

2a2

=

5

2

(

kq2

a2

)
where k =

1

4πε

. Here, as shown in the figure, line AB divided the soap film into two equal parts. The free-body diagram of half part is also depicted in the figure here.

At equilibrium, the surface tension balances the force.
Therefore,
F‌surface = 2√2αγ
That is, 2√2αγ =

5

2

(

kq2

a2

)
⇒ a3 =

5

4√2

(

q2

γ

)
Therefore,
a = Any constant × (

q2

γ

)

1

3

Hence, N = 3.