Question

A charged sphere of mass 2.8 × 10⁻⁴ kg is suspended from a string. An electric force acts horizontally on the sphere so that the string makes an angle of 33° with the vertical when at rest. Find:

(a) The magnitude of the electric force.

A) 1.2 × 10⁻⁴ N
B) 2.4 × 10⁻⁴ N
C) 3.6 × 10⁻⁴ N
D) 4.8 × 10⁻⁴ N

Answer 1

The magnitude of the electric force acting on the charged sphere is 2.4 × 10⁻⁴ N.

Step-by-step explanation:

To find the magnitude of the electric force acting on the charged sphere, we can use trigonometry and Newton's second law. The weight of the sphere acts vertically downward, while the electric force acts horizontally. The string makes an angle of 33° with the vertical when the sphere is at rest. Using the given mass of the sphere (2.8 × 10⁻⁴ kg) and the angle, we can find the tension in the string. This tension is equal to the magnitude of the electric force.

By resolving the forces, we have the equation T cos θ = mg and T sin θ = Fe (where T is the tension, θ is the angle, m is the mass of the sphere, g is the acceleration due to gravity, and Fe is the electric force). Solving these equations simultaneously, we can find the magnitude of the electric force.

Substituting the given values into the equations and solving for Fe, we get:

Fe = T sin θ = (mg) sin θ = (2.8 × 10⁻⁴ kg) × (9.8 m/s²) × sin(33°) = 2.4 × 10⁻⁴ N