Two pith-balls each weighing 10-3 kg are suspendede from the same point by means of silk threads 0.5m long. On charging the pith-balls equally, they are found to repel each other to a distance of 0.2m. Calculate the charge on each ball.
Please solve this sum
Each pith ball will be 0.2/2 = 0.1 m from the vertical centre line.
The vertical component of tension in the string is equal to the weight of a pith ball.
Ty = Tsinθ, where θ is the angle made by string with horizontal.
Hypotenuse = Length of the string = 0.5 m
Adjacent side = 0.1 m
Opposite side = (0.52-0.12)1/2 = 0.49
Ty = Tsinθ = W = 10-3x10 N
T = (10-3x10)/(0.49/0.5) = 10.20x10-3
The horizontal component of tension is the electrostatic force of repulsion,
kq2/r2 = Tx = Tcosθ = 10.20x10-3 (0.1/0.5)
q2 = (10.20x10-3 )(0.1/0.5)(0.22)/(9x109) = 0.009x10-12
q = 0.09 x 10-6 C
q = 90 nC.