Question

Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side ‘a’. The surface tension of the soap film is . The system of charges and planar film are in equilibrium, and, where ‘k’ is a constant. Then N is

Answer 1

first of all find net electrostatic force at any corner of square.
see attachment , here a rough diagram is shown . You can easily understand how much net electrostatic force at A .
e.g., Fnet = F₃ + √(F₁² + F₂²)
F₃ = Kq²/2a²
F₁ = F₂ = kq²/a
∴ Fnet = Kq²/2a² + √2Kq²/a²
= q²/a² [K/2 + √2K]
= q²/a² × constant [∵ (K/2 + √2K) is Constant term ]

Now, net force = force on bubble
= Surface tension × side length
= γa
∴ q²/a² × Constant = γa
⇒ a³ = q²/γ × Constant
⇒ a = [q²/γ × constant ]⅓
=K [q²/γ]⅓ , here is Constant not kappa Constant.
Now compare it with a = [q²/γ]^{1/N}
Hence, n = 3