We are given the mass of each ball, m = 0.1*10^-3 kg, and we know that the force due to gravity on each ball is given by the weight, W = m * g, where g is the acceleration due to gravity. Since the balls are identical and the charges are equal, the gravitational force acting on each ball is the same, so W1 = W2 = 9.81 * 0.1 * 10^-3 N.
Let's call the charge on each ball q. Since both balls have the same charge, the electrostatic force acting between them is given by Coulomb's Law: Fe = k * q^2 / r^2, where k is the Coulomb's constant (k = 8.99 * 10^9 N m²/C²), q is the charge on each ball, and r is the distance between the centers of the balls.
At equilibrium, the forces acting on each ball are balanced, so the net force acting on a ball is zero. This means that the forces acting on a ball due to gravity and charge must be equal and opposite: Fe = W.
Now we can solve for q:
Fe = W
k * q^2 / r^2 = m * g
q^2 = (m * g * r^2) / k
The given information is not enough to solve for the charge magnitude since we don't know the length of the threads or the distance between the centers of the balls (r). If we were given the length of the threads and the angle formed between the vertical and the threads or other related parameters, we can solve for the distance 'r' and hence the charge q.
Two identical balls each of mass 0.1*10-3kg carry identical charges and are suspended by two non conducting threads of equal length. At equilibrium they position themselves. Calculate the charge on either ball.
1 answer