A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinder is doubled, what happens to the electric field at the surface?
Practice Questions
1 question
Q1
A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinder is doubled, what happens to the electric field at the surface?
It doubles
It halves
It remains the same
It becomes zero
The electric field due to a uniformly charged infinite cylinder depends only on the charge per unit length, not on the radius.
Questions & Step-by-step Solutions
1 item
Q
Q: A cylindrical Gaussian surface encloses a charge Q. If the radius of the cylinder is doubled, what happens to the electric field at the surface?
Solution: The electric field due to a uniformly charged infinite cylinder depends only on the charge per unit length, not on the radius.
Steps: 5
Step 1: Understand that we have a cylindrical Gaussian surface that encloses a charge Q.
Step 2: Recognize that the electric field around a charged object depends on the charge and the distance from the charge.
Step 3: Note that for a cylindrical charge, the electric field is determined by the charge per unit length (Q/L) and not the radius of the cylinder.
Step 4: Realize that if we double the radius of the cylinder, the charge per unit length remains the same because the total charge Q is unchanged.
Step 5: Conclude that since the electric field depends only on the charge per unit length, the electric field at the surface of the cylinder does not change when the radius is doubled.
