Question

Two pith balls, each with a mass of 1.4 g, are attached to non-conducting threads and suspended from a common hook. Each thread has a length of 28.8 cm. The balls are then given an identical charge, which causes them to separate. In equilibrium, the threads are separated by an angle of 3.3°. Calculate the charge on each pith ball, in coulombs (C).

Answer 1

The charge on each pith ball is approximately 4.32 x 10^-8 C.

Step-by-step explanation:

To calculate the charge on each pith ball, we can use Coulomb's Law. Coulomb's Law states that the 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. In this case, we have two pith balls with identical charges and separated by a certain distance.

Using the given information, we can calculate the charge on each pith ball as follows:

1. First, we need to calculate the force between the pith balls. The force can be calculated using Coulomb's Law: F = k * (q1 * q2) / r^2, where F is the force, k is the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2), q1 and q2 are the charges on the pith balls, and r is the distance between them.
2. Next, we can equate the force to the tension in the threads. Since the two pith balls are in equilibrium, the tension in their threads must be equal and opposite. Therefore, we can write: T1 = T2. The tension in a thread can be calculated using the equation: T = mg*cos(θ), where T is the tension, m is the mass of the pith ball, g is the acceleration due to gravity, and θ is the angle the thread makes with the vertical.
3. Finally, we can solve the equations simultaneously to find the charge on each pith ball.

Plugging in the given values, we can calculate the charge on each pith ball as: q = sqrt((T*4*r^2) / (m*g*k)).

Substituting the values, we get: q = sqrt((2*1.4*9.8*0.288^2) / (0.0014*8.99*10^9))

Solving this equation, we find that the charge on each pith ball is approximately 4.32 x 10^-8 C.