If the ball is in equilibrium when the string

makes a 43◦
angle with the vertical as indicated, what is the net charge on the ball? The
acceleration due to gravity is 9.81 m/s
2.
Answer in units of C

To determine the net charge on the ball, we need to apply the concept of electrostatics and equilibrium.

In this scenario, the ball is in equilibrium, meaning the forces acting on it must balance. The two forces acting on the ball are the gravitational force (mg) pulling it downwards and the electrostatic force (Fe) exerted by the net charge on the ball, pulling it upwards along the string.

Since the ball is in equilibrium, the vertical components of these forces must balance:

mg * cos(43°) = Fe

Now, let's break down these forces:

1. Gravitational Force (mg):
The gravitational force is given by the equation F = mg, where m is the mass of the ball and g is the acceleration due to gravity (9.81 m/s^2).

2. Electrostatic Force (Fe):
The electrostatic force is calculated using Coulomb's Law, which states that Fe = k * (q1 * q2) / r^2, where k is the electrostatic constant (9 × 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between them. In this case, q2 is the net charge on the ball, and q1 is assumed to be zero since there is no mention of any other charges nearby.

Now, let's put all the values into the equation:

mg * cos(43°) = k * (q * 0) / r^2

Simplifying the equation further:

mg * cos(43°) = 0

Since the right-hand side of the equation is zero, we can conclude that there is no net charge (q) on the ball to maintain equilibrium in this particular case.

Therefore, the net charge on the ball is 0 C.