Two balls of same mass and carrying equal charge are hung from a fixed support of length l . At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, x between

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Two balls of same mass and carrying equal charge are hung from a fixed support of length l . At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, x between the balls is proportional to :

TestHub · Accepted Answer

In equilibrium, F e ​ = T sin θ m g = T cos θ tan θ = m g F e ​ ​ = 4 π ϵ 0 ​ x 2 × m g q 2 ​ also tan θ ≈ sin = ℓ x /2 ​ Hence, 2 ℓ x ​ = 4 π ϵ 0 ​ x 2 × m g q 2 ​ ⇒ x 3 = 4 π ϵ 0 ​ m g 2 q 2 ℓ ​ ∴ x = ( 2 π ϵ 0 ​ m g q 2 ℓ ​ ) 1/3 Therefore x ∝ ℓ 1/3

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