A cylindrical Gaussian surface of length L and radius R encloses a charge Q. Wha
Practice Questions
Q1
A cylindrical Gaussian surface of length L and radius R encloses a charge Q. What is the electric field E at a distance R from the axis of the cylinder?
Q/(2πε₀R)
Q/(4πε₀R²)
Q/(ε₀L)
0
Questions & Step-by-Step Solutions
A cylindrical Gaussian surface of length L and radius R encloses a charge Q. What is the electric field E at a distance R from the axis of the cylinder?
Correct Answer: E = Q/(2πε₀L)
Step 1: Understand that we have a cylindrical Gaussian surface with a charge Q inside it.
Step 2: Recognize that the electric field E we want to find is at a distance R from the axis of the cylinder.
Step 3: Recall Gauss's law, which states that the electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space (ε₀).
Step 4: For a long charged cylinder, the electric field is uniform and points radially outward from the axis.
Step 5: Set up the Gaussian surface: a cylinder of length L and radius R that surrounds the charged cylinder.
Step 6: Calculate the electric flux through the curved surface of the Gaussian cylinder, which is E times the surface area (2πRL).
Step 7: According to Gauss's law, set the electric flux equal to the enclosed charge divided by ε₀: E(2πRL) = Q/ε₀.
Step 8: Solve for the electric field E: E = Q/(2πε₀L).
Step 9: Conclude that this formula gives the electric field E at a distance R from the axis of the cylinder for points outside the cylinder.
Gauss's Law – The relationship between electric flux through a closed surface and the charge enclosed by that surface.
Electric Field of a Cylinder – Understanding how to calculate the electric field around a cylindrical charge distribution.
