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

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 $a = k {(\frac{q^{2}}{γ})}^{1 / N},$ where $' k'$ is a constant. Then $N$ is [2011]

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(3)

Net electrostatic force on one charge due to remaining three charges

$' a'$

Surface tension force $F_{s t} = γ a$

In equilibrium,

$\frac{q^{2}}{a^{2}} \times constant = γ a$

$∴$ $a = k {(\frac{q^{2}}{γ})}^{1 / 3}$

$∴$ $N = 3$

Solution

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Solution

Q. 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(q2γ)1/N, where 'k' is a constant. Then N is [2011]

Ans. (3) Net electrostatic force on one charge due to remaining three charges Felectro=kq22a2+2[kq2a2×12]=q2a2×constant Surface tension force Fst=γa In equilibrium, q2a2×constant=γa ∴ a=k(q2γ)1/3 ∴ N=3

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