A small m = 2.00 g plastic ball is suspended by a L = 24.0 cm long string in a uniform electric field, as shown in Figure P15.50. If the ball is in equilibrium when the string makes a 18.0° angle with the vertical as indicated, what is the net charge on the ball?

To slove as listed, you need to know the charge of the Electric Field:

Fx=Fy
Eqsin(18)= mgcos(18)

q=mgcos(18)/ Esin(18)

since cos/sin= tan

q= mg tan(18)/E

To find the net charge on the ball, we need to use the concept of electric force and gravitational force acting on the ball.

We know that the ball is in equilibrium, so the electric force acting on the ball is equal in magnitude and opposite in direction to the gravitational force acting on it.

Let's break down the forces acting on the ball:

1. Gravitational force (Fg):
The gravitational force acting on the ball is given by the formula: Fg = m * g
where m is the mass of the ball (2.00 g) and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Fg = (2.00 g) * (9.8 m/s^2)

2. Electric force (Fe):
The electric force acting on the ball is given by the formula: Fe = q * E
where q is the charge on the ball and E is the magnitude of the electric field.

Since the ball is in equilibrium, the angle between the string and the vertical is the same as the angle between the electric field and gravity (18.0°).

tan(18.0°) = E / g
E = g * tan(18.0°)

3. Equilibrium condition:
Since the ball is in equilibrium, Fe = Fg.

Substituting the formulas for Fg and Fe into the equilibrium condition equation:

q * g * tan(18.0°) = m * g

We can cancel out the gravitational acceleration (g) on both sides:

q * tan(18.0°) = m

Now we can solve for the charge, q:

q = m / tan(18.0°)

Using the given values:

q = (2.00 g) / tan(18.0°)

Calculating this will give us the net charge on the ball.

To find the net charge on the plastic ball, we need to take into account the forces acting on it and use the concept of equilibrium.

In this scenario, the forces acting on the plastic ball are its weight (mg) acting downwards and the electric force (Fe) acting towards the left, parallel to the string. The tension in the string (T) acts towards the right, perpendicular to the string.

In equilibrium, the net force acting on the ball is zero. So we can set up the following equation:

T * sinθ = Fe

where T is the tension in the string and θ is the angle the string makes with the vertical.

The tension in the string can be calculated using the following equation:

T = mg / cosθ

where m is the mass of the ball, g is the acceleration due to gravity, and θ is the angle the string makes with the vertical.

Substituting the value of T in the first equation, we get:

mg / cosθ * sinθ = Fe

Now, the electric force (Fe) can be calculated using the following formula:

Fe = q * E

where q is the charge on the ball and E is the electric field strength.

Substituting the value of Fe in the previous equation, we have:

mg / cosθ * sinθ = q * E

Now, we can rearrange the equation to solve for the charge on the ball (q):

q = (mg * sinθ) / (cosθ * E)

Substituting the given values:

m = 2.00 g = 0.002 kg (Convert grams to kilograms)
g = 9.8 m/s^2 (acceleration due to gravity)
θ = 18.0°
E = ? (electric field strength)

To find the electric field strength (E), we need additional information or another equation. Please provide any additional details or equations if available.