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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 γ. The system of charges and planar film are in equilibrium, and a = k[q²/γ]^(1/N), where 'k' is a constant. Then N is:

2

9

3

4

Solution:

Net electrostatic force on one charge = (1/4πε₀)(q²/a²)[1/2 + √2]
Considering MN as system,
(1/4πε₀)(q²/a²)[1/2 + √2] * 2cos45° = 2γa
or a = k[q²/γ]^(1/3)
Thus N = 3