A point charge of +Q is placed at the center of a spherical Gaussian surface. Wh
Practice Questions
Q1
A point charge of +Q is placed at the center of a spherical Gaussian surface. What is the total electric flux through the surface?
0
Q/ε₀
Q/2ε₀
4πQ/ε₀
Questions & Step-by-Step Solutions
A point charge of +Q is placed at the center of a spherical Gaussian surface. What is the total electric flux through the surface?
Step 1: Understand that a point charge of +Q is placed at the center of a spherical surface.
Step 2: Recall Gauss's law, which states that the total electric flux (Φ) through a closed surface is equal to the charge enclosed (Q_enc) divided by the permittivity of free space (ε₀).
Step 3: Identify the charge enclosed by the Gaussian surface. In this case, the charge enclosed (Q_enc) is +Q.
Step 4: Substitute the value of Q_enc into Gauss's law formula: Φ = Q_enc/ε₀.
Step 5: Replace Q_enc with +Q in the formula: Φ = Q/ε₀.
Step 6: Conclude that the total electric flux through the spherical surface is Φ = Q/ε₀.
Gauss's Law – Gauss's law relates the electric flux through a closed surface to the charge enclosed by that surface.
