Using Gauss's law, what is the electric field inside a uniformly charged cylindrical shell of radius R?
Practice Questions
1 question
Q1
Using Gauss's law, what is the electric field inside a uniformly charged cylindrical shell of radius R?
0
Q/(2πε₀R)
Q/(4πε₀R²)
Q/(2πε₀R²)
Inside a uniformly charged cylindrical shell, the electric field is zero due to symmetry, as the contributions from all parts of the shell cancel out.
Questions & Step-by-step Solutions
1 item
Q
Q: Using Gauss's law, what is the electric field inside a uniformly charged cylindrical shell of radius R?
Solution: Inside a uniformly charged cylindrical shell, the electric field is zero due to symmetry, as the contributions from all parts of the shell cancel out.
Steps: 7
Step 1: Understand Gauss's Law, which states that the electric flux through a closed surface is proportional to the charge enclosed by that surface.
Step 2: Consider a cylindrical shell with a uniform charge distribution and a radius R.
Step 3: Visualize a point inside the cylindrical shell. This point is at a distance less than R from the center of the shell.
Step 4: Choose a Gaussian surface, which is an imaginary cylinder that is also inside the shell and has a radius less than R.
Step 5: Calculate the charge enclosed by the Gaussian surface. Since the point is inside the shell, there is no charge enclosed (the charge is only on the shell).
Step 6: According to Gauss's Law, since the enclosed charge is zero, the electric flux through the Gaussian surface is also zero.
Step 7: Since the electric flux is zero, the electric field inside the shell must also be zero, as there are no contributions from the shell's charge.
