IIT-JEE 2011 · Paper 1 · Physics Q42

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PhysicsInteger+4Question 42 of 69

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 $\gamma$ . The system of charges and planar film are in equilibrium, and $a=k\left[\dfrac{q^2}\gamma\right]^{1/N}$ , where ' $k$ ' is a constant. Then $N$ is

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Answer and worked solution

Official answer: 3

Balance of forces on a corner charge: the Coulomb repulsion $\sim\dfrac{q^2}{\varepsilon_0a^2}$ is balanced by the film's surface tension acting over a length $\sim a$ , i.e. $\sim\gamma a$ .

So $a^3\propto\dfrac{q^2}\gamma$ and $N=3$ .

Answer: 3

Topics:Surface tension Coulomb's law and superposition

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IIT-JEE 2011 · Paper 1, Physics question 42