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?
Practice Questions
1 question
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
The electric flux through the curved surface is proportional to the charge enclosed, which remains constant, so the flux through the curved surface doubles if the height is doubled.
Questions & Step-by-step Solutions
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Q
Q: 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?
Solution: The electric flux through the curved surface is proportional to the charge enclosed, which remains constant, so the flux through the curved surface doubles if the height is doubled.
Steps: 6
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.
