# Magnitude of the Charge on Each Ball

1. Sep 27, 2009

### chunkytuna21

Two 2.5 g pith balls hang in air on cotton threads 48 cm long from a common point of support. The balls are then equally charged and they spring apart, each making an angle of 10° with the vertical. Find the magnitude of the charge on each ball.

F = (k q1 q2) / r^2

Q1 and Q2 are the same so
F = (k q^2) / r^2
q = sqrt[ (F r^2) / k ]

where r is the distance between the balls (taken as point charges)

Using cosine rule, a^2 = b^2 + c^2 - 2 b c cosA
where a = r
b and c = 0.48m
A = 10 degrees
a = sqrt( 2 * 0.48^2 - 2 * 0.48^2 * cos 10)
r = 0.0083669513m

F = force on each ball
F = mass * acceleration due to gravity * sin (5 degrees)
F = 0.0025kg * 9.81 * sin(5)
F = 2.14 * 10^-3

k = electrostatic constant = 9 * 10^9 N m^2 C^-2

so q = sqrt[ (F r^2) / k ]
q = sqrt[ (2.14 * 10^-3 x 0.0083669513^2) / 9 * 10^9]
q = sqrt( 1.664584116E-17)

q = 4.1E-9 C

I have tried almost everything, but I keep getting the wrong answer. Where am I going wrong? Am I even on the right track? Any help would be greatly appreciated.

2. Sep 27, 2009

### rl.bhat

1) Each ball makes an angle 10 degrees with the vertical..
2) In equilibrium position, three forces are acting on the ball. Identify them.
3) Resolve them and equate net Fx = 0 and net Fy = 0