Question

Some General Problems of Electrostatics.

Answer 1

\(\large \sf Suspended~Charged~ball~system\)

Answer 2

Two balls of similar charge q and mass m are suspended by two ropes from same point. Find the angle Θ, Tension T and distance between the centers of the ball.

Answer 3

\(\sf Finding~Θ\)

TcosΘ=mg
TsinΘ=\(\sf F_c=\large\frac{kq^2}{r^2}\)

--> tanΘ=\(\large\sf \frac{kq^2}{mg\times r^2}\\or~Θ=tan^{-1}\large \frac{kq^2}{mg\times r^2}\)

Answer 4

\(\large \sf Finding~Tension\)

TcosΘ=mg
TsinΘ=\(\sf F_c=\large\frac{kq^2}{r^2}\)

--> \(\sf T^2sin^2Θ +T^2cos^2Θ=F_c^2+(mg)^2\\T^2(sin^2Θ+cos^2Θ)=F_c^2+(mg)^2\\T(1)=\sqrt{F_c^2+(mg)^2}\\or~\boxed{T=\sqrt{F_c^2+(mg)^2}} \)

Answer 5

\(\large \sf Finding~distance~between~balls\)

Answer 6

If distance between two charges is r and distance between the center of ball and the point from it is hanged is l. Then,

\(\large\sf \frac{r/2}{l}=sinΘ=tanΘ=\frac{kq^2}{r^2\times mg}\\ -->\huge \boxed{r=[\frac{kq^22l}{mg}]^{1/3}}\)

Answer 7

I originally encountered this as a problem where you're at a birthday party and at the ceiling there are three balloons hanging which are all equally statically charged. Find the separation of the balloons. It gave some other information, but it is essentially the same as this with a 3rd particle involved, interesting to look into as well!

Very good guide @Abhisar helped me review! Thanks!

Answer 8

Thanks @kainui