A cube encloses a charge Q at its center. What is the electric flux through one face of the cube?
Practice Questions
1 question
Q1
A cube encloses a charge Q at its center. What is the electric flux through one face of the cube?
Q/ε₀
Q/6ε₀
Q/3ε₀
Zero
The total flux through the cube is Q/ε₀, and since there are 6 faces, the flux through one face is Q/6ε₀.
Questions & Step-by-step Solutions
1 item
Q
Q: A cube encloses a charge Q at its center. What is the electric flux through one face of the cube?
Solution: The total flux through the cube is Q/ε₀, and since there are 6 faces, the flux through one face is Q/6ε₀.
Steps: 6
Step 1: Understand that a cube has 6 faces and encloses a charge Q at its center.
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) divided by the permittivity of free space (ε₀).
Step 3: Apply Gauss's Law to the cube: The total electric flux through the entire cube is Φ = Q/ε₀.
Step 4: Since the cube has 6 identical faces, the electric flux is evenly distributed across all faces.
Step 5: To find the electric flux through one face, divide the total flux by the number of faces: Φ_face = (Q/ε₀) / 6.
Step 6: Simplify the expression: Φ_face = Q / (6ε₀).
