A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinde
Practice Questions
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
Questions & Step-by-Step Solutions
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?
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.
Gauss's Law – The relationship between electric flux through a closed surface and the charge enclosed by that surface.
Electric Flux – The measure of the quantity of electric field lines passing through a surface.
Cylindrical Symmetry – Understanding how electric fields behave in cylindrical geometries.
