If a charge of +Q is placed at one corner of a cube, what is the total electric flux through the entire surface of the cube?
Practice Questions
1 question
Q1
If a charge of +Q is placed at one corner of a cube, what is the total electric flux through the entire surface of the cube?
Q/ε₀
Q/6ε₀
0
Q/4ε₀
The total electric flux through the cube is Q/ε₀, but since only 1/6 of the charge is enclosed by the cube, the flux is Q/6ε₀.
Questions & Step-by-step Solutions
1 item
Q
Q: If a charge of +Q is placed at one corner of a cube, what is the total electric flux through the entire surface of the cube?
Solution: The total electric flux through the cube is Q/ε₀, but since only 1/6 of the charge is enclosed by the cube, the flux is Q/6ε₀.
Steps: 9
Step 1: Understand that electric flux is related to the charge enclosed by a surface.
Step 2: Recall Gauss's Law, which states that the total electric flux (Φ) through a closed surface is equal to the charge (Q) enclosed divided by the permittivity of free space (ε₀).
Step 3: In this case, we have a charge of +Q placed at one corner of a cube.
Step 4: Visualize the cube: since the charge is at a corner, only a fraction of the charge is actually inside the cube.
Step 5: Determine how much of the charge is inside the cube: since the charge is at a corner, only 1/8 of the charge would be inside if the cube were divided into 8 smaller cubes.
Step 6: However, since we are considering the entire cube and the charge is at the corner, we need to consider that the cube shares this corner with 6 other cubes.
Step 7: Therefore, the fraction of the charge that is effectively enclosed by the cube is 1/6.
Step 8: Now, apply Gauss's Law: the total electric flux through the cube is Φ = (Q/6) / ε₀.
