Final answer:
The net charge on the ball is found by using the equilibrium conditions to balance the gravitational and electric forces, resulting in a charge of approximately 8.2 microCoulombs.
Step-by-step explanation:
The student is asking about the net charge on a plastic ball in a uniform electric field. To find the charge, we need to consider the forces acting on the ball in equilibrium. We know the mass of the ball (16 g), the angle the string makes with the vertical (30°), and the electric field's magnitude (1.1 x 103 N/C).
There are two forces acting on the ball: the gravitational force downward (mg) and the electric force (qE) horizontally. Since the ball is in equilibrium, these forces will balance each other out. The electric force provides the horizontal component, while the gravitational force provides the vertical component of the tension in the string.
The tension T in the string can be decomposed into a vertical component Tcos(θ), balancing the weight mg, and a horizontal component Tsin(θ), balancing the electric force qE.
Using trigonometry and Newton's second law, we can set up the following equations:
- Tcos(30°) = mg
- Tsin(30°) = qE
By dividing the second equation by the first, we get:
tan(30°) = (qE)/(mg)
From which we can solve for the net charge q:
q = mg*tan(30°)/E
Now, we insert the given values:
q = (0.016 kg)(9.81 m/s2)*tan(30°)/(1.1 x 103 N/C)
q ≈ 8.2 x 10-6 C
Thus, the net charge on the ball is approximately 8.2 μC (microCoulombs).