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 a=k [ q^2 ]^ 1 / N , where k is a constant. Then, N is

Step-by-step solution

F₁= Net electrostatic force on anyone charge due to rest of three charges = 1 4 ₀ q^2 a^2 ( 2 + 1 2 ) F₂= Surface tension force = a If we see the equilibrium of line B C , then, 2 F₁ 45^ =F₂ or 2 F₁=F₂ or 1 4 ₀ q^2 a^2 (2+ 1 2 )= a a^3= 1 4 ₀ (2+ 1 2 ) q^2 or a= 1 4 ₀ (2+ 1 2 ) ^ 1 / 3 [ q^2 ]^ 1 / 3 =k [ q^2 ]^ 1 / 3 where, k= 1 4 ₀ (2+ 1 2 ) ^ 1 / 3 Therefore, N=3 Answer is 3 . Analysis of Question (i) Question is moderately difficult. (ii) In my opinion problems of surface tension or viscosity are always not ver