Two 5.0 g point charges on 1.0-m -long threads repel each...

Two $5.0 \mathrm{g}$ point charges on $1.0-\mathrm{m}$ -long threads repel each other after being charged to $+100 \mathrm{nC}$, as shown in Figure P26,59. What is the angle $\theta$ ? You can assume that $\theta$ is a small angle.
(FIGURE CANNOT COPY)

Key Concepts

Small Angle Approximation

The small angle approximation assumes that for small angles (measured in radians), the sine and tangent of the angle are approximately equal to the angle itself. This simplifies mathematical calculations in many physics problems, including those involving small displacements of pendulum-like systems, by reducing complex trigonometric functions to linear expressions.

Pendulum Geometry

The arrangement involves simple pendulum mechanics where a suspended object makes an angle with the vertical due to a horizontal force. Understanding the geometric relationship between the length of the pendulum string, the displacement angle, and the horizontal force component is essential. This analysis allows one to derive the expression for the angle as a function of the forces acting on the suspended charge.

Coulomb's Law

Coulomb's law describes the force between two charged objects. It states that the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance separating them. This principle is crucial for calculating the repulsive force acting between similar charges in the scenario.

Force Equilibrium

In problems where objects are suspended and subject to multiple forces, force equilibrium is used to analyze the balance of forces. In the context of the charged masses, the upward tension in the threads balances the gravitational force, while the horizontal component of tension counteracts the electrostatic repulsive force. Setting these forces equal allows for solving the angle related to the displacement of the masses.

Transcript

Please give Ace some feedback