Question #182872

Two small conducting balls of identical mass m and charge q hang from non-conducting rope of length L Assume that Ɵ is very small tanƟ = sinƟ. Find an expression for the equilibrium separation x of the balls.


1
Expert's answer
2021-04-26T16:59:56-0400

Answer

Tension in rope

By vertical equilibrium

T=mgcosθT=\frac{mg}{cos\theta}

By equilibrium

kq2L2sin2θ=Tsinθ\frac{kq^2}{L^2sin^2\theta}=Tsin{\theta}


And

kq2L2sin2θ=mgcosθsinθ\frac{kq^2}{L^2sin^2\theta}=\frac{mg}{cos\theta}sin{\theta}


kq24(L2sin2θ)=mgtanθ\frac{kq^2}{4(L^2sin^2\theta)}=mgtan{\theta}




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