A charge q = 2.00 μC is placed at the origin in a region where there is already a uniform electric field = (100 N/C) .Calculate the flux of the net electric field through a Gaussian sphere of radius R = 10.0 cm centered at the origin.(ε₀ = 8.85 × 10^-12 C²/N • m²) A) 5.52 × 10⁵ N • m²/C B) 1.13 × 10⁵N • m²/C C) 2.26 × 10⁵ N • m²/C D) zero

Question

Quizplus · Accepted Answer

The flux of the net electric field through a Gaussian surface of radius R centered at the origin is given by:
Φ = E•A = EAcosθ
where E is the electric field, A is the area of the Gaussian sphere (4πR2), and θ is the angle between E and the normal to the surface.
Since the electric field is uniform, its magnitude is the same at every point on the Gaussian surface. Therefore, we can take it out of the integral, and we only need to calculate the component of the area vector perpendicular to the electric field:
Φ = E•A = E(4πR2cosθ) = (100 N/C)(4π(0.1 m)2) = 1.13 × 105 N·m2/C
The electric flux is positive since the charge q is positive and the electric field points away from the charge. Therefore, the correct answer is C.

A Charge Q = 2