A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinder is r and its height is h, what is the electric flux through the curved surface?
Practice Questions
1 question
Q1
A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinder is r and its height is h, what is the electric flux through the curved surface?
Q/ε₀
Q/(2ε₀)
Q/(4ε₀)
0
The electric flux through the curved surface of a cylinder is given by Φ = Q_enc/ε₀, where Q_enc = Q.
Questions & Step-by-step Solutions
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Q
Q: A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinder is r and its height is h, what is the electric flux through the curved surface?
Solution: The electric flux through the curved surface of a cylinder is given by Φ = Q_enc/ε₀, where Q_enc = Q.
Steps: 6
Step 1: Understand that we have a cylindrical Gaussian surface that encloses a charge Q.
Step 2: Recognize that the electric flux (Φ) through a surface is related to the charge enclosed (Q_enc) by the formula Φ = Q_enc/ε₀, where ε₀ is the permittivity of free space.
Step 3: Since the entire charge Q is enclosed by the cylindrical surface, we set Q_enc = Q.
Step 4: Substitute Q_enc into the electric flux formula: Φ = Q/ε₀.
Step 5: Note that the formula gives us the total electric flux through the entire surface of the cylinder, but we are specifically interested in the curved surface.
Step 6: For a cylindrical surface, the electric field is uniform and perpendicular to the curved surface, so the flux through the curved surface can be calculated using the same formula.
