A cylindrical Gaussian surface encloses a charge Q. If the height of the cylinde
Practice Questions
Q1
A cylindrical Gaussian surface encloses a charge Q. If the height of the cylinder is doubled while keeping the radius constant, what happens to the electric flux through the curved surface?
It doubles
It halves
It remains the same
It becomes zero
Questions & Step-by-Step Solutions
A cylindrical Gaussian surface encloses a charge Q. If the height of the cylinder is doubled while keeping the radius constant, what happens to the electric flux through the curved surface?
Correct Answer: Electric flux through the curved surface doubles.
Step 1: Understand that electric flux is related to the charge enclosed by a surface.
Step 2: Recognize that the charge Q inside the cylindrical Gaussian surface does not change when the height is doubled.
Step 3: Know that the electric flux through the curved surface of the cylinder is given by the formula: Flux = Electric Field (E) × Area (A).
Step 4: The area of the curved surface of a cylinder is calculated as: Area = 2πrh, where r is the radius and h is the height.
Step 5: If the height (h) of the cylinder is doubled, the new area of the curved surface becomes: New Area = 2πr(2h) = 4πrh, which is double the original area.
Step 6: Since the electric field (E) remains constant (as the charge enclosed is constant), the electric flux through the curved surface also doubles because Flux = E × New Area.
Gauss's Law – The electric flux through a closed surface is proportional to the charge enclosed within that surface.
Electric Flux – Electric flux is defined as the product of the electric field and the area through which it passes, and it is affected by the geometry of the surface.
Cylindrical Symmetry – In cylindrical coordinates, the electric field due to a point charge or a line charge can be analyzed using cylindrical Gaussian surfaces.
