Electric Flux and Charge Calculation

What is the electric flux through the surface of a sphere with a point charge at its center and a radius of 0.149 m?

Choose one:

A. 1.29×10^6 N·m²/C

B. 1.88×10^5 N·m²/C

C. 0.279 m²

D. 3.75×10^-5 C

Answer:

The electric flux through the surface of a sphere with the given charge at its center and a radius of 0.149 m is 1.88×10^5 N·m²/C.

Electric flux is a crucial concept in physics, specifically in the field of electromagnetism. It helps us understand the flow of electric field through a surface. In this scenario, we are focused on determining the electric flux through a sphere with a point charge at its center.

The electric flux through the surface of a sphere can be calculated using the formula Φ = E * A * cos(θ), where E is the electric field, A is the area of the surface, and θ is the angle between the electric field and the normal to the surface.

Given that the electric field is 1.29×10^6 N/C and the radius of the sphere is 0.149 m, we can calculate the area of the sphere's surface using the formula A = 4πr². Substituting the values, we find that the area is approximately 0.279 m².

By applying the formula for electric flux and considering the radial nature of the electric field, we determine that the electric flux through the sphere's surface is 1.88×10^5 N·m²/C.

Furthermore, to find the magnitude of the charge, we utilize the equation Q = Φ * ε₀, where Q represents the charge and ε₀ is the electric constant. By substituting the values of electric flux and ε₀ into the formula, we calculate that the magnitude of the charge is 3.75×10^-5 C.

Understanding the relationship between electric flux and charge is essential for grasping the behavior of electric fields and charges in various systems. By studying these fundamental concepts, we can delve deeper into the mysteries of electromagnetism and its applications in modern technology.