Q.

Four-point charges, each of charge +q, are rigidly fixed at the four corners of a square planar soap film of side 'σ' . The surface tension of the soap film is a. If the system of charges and planar film are in equilibrium, then side of square is givenas a=14π∈01+122⋅q2σ1/N, find the value of N.

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answer is 3.00.

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Detailed Solution

F2=q24πε0(2a)2=q24πε0×2a2Net force on side AB of the film, F=2F1+2F2cos ⁡45⇒F=2q24πε0a2+2q24πε022a2=q24πε0a22+12Force on AB due to surface tension=2σaq24πε0a22+12=2σa⇒ a=14πϵ01+122⋅q2σ1/3               ......(i)Given that a=14πϵ01+122⋅q2σ1/N      …….(ii)Comparing Eqs. (i) and (ii), we have N=3
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