Two equally charged balls, each of mass 0.10 gm, are suspended from the same point by threads 13 cm long. The balls come to rest 10 cm apart due to electrostatic repulsion. Determine the charge on each ball.
note 5 12 13 right triangle here
Fh = k Q1 Q2/d^2 horizontal electrostatic
Fd = m g gravity down
T = tension
T(12/13) = m g
T(5/13) = Fh
12 T = 13 m g
5 T = 13 Fh
12/5 = m g/Fh
Fh = (5/12) m g
so
9^10^9 Q^2/.1^2 = (5/12)(.0001)(9.8)
solve for Q
thats wrong
To determine the charge on each ball, we can use Coulomb's law, which states that the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's break down the problem step by step:
Step 1: Calculate the gravitational force between the balls.
Since the balls are stationary, the gravitational force is balanced by the tension in the threads. Using the formula for gravitational force, F_g = m * g, where m is the mass of each ball and g is the acceleration due to gravity (approximately 9.8 m/s^2), we can calculate the gravitational force.
F_g = (0.10 g) * (9.8 m/s^2) = 0.98 * 10^(-3) N
Step 2: Calculate the electrostatic force between the balls.
The electrostatic force between the balls is repulsive because they have the same charge. Using Coulomb's law, F_e = k * (q^2 / r^2), where k is the electrostatic constant (k = 8.99 * 10^9 Nm^2/C^2), q is the magnitude of the charge on each ball, and r is the separation distance between the balls, we can calculate the electrostatic force.
F_e = k * (q^2 / r^2)
Here, we need to calculate the charge, q.
Step 3: Equate the electrostatic force and gravitational force.
Since the balls are in equilibrium, the electrostatic force and the gravitational force are equal in magnitude.
F_e = F_g
k * (q^2 / r^2) = m * g
Step 4: Solve for the charge on each ball.
Rearranging the equation, we get:
q^2 = (m * g * r^2) / k
q = sqrt((m * g * r^2) / k)
q = sqrt((0.10 g * 9.8 m/s^2 * (0.13 m)^2) / (8.99 * 10^9 Nm^2/C^2))
Calculating this equation will give you the charge on each ball.