Question

A cylindrical shell of radius 7.00 cm and length 2.59 m has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 20.1 cm radially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C.

A) Use approximate relationships to find the net charge on the shell.
B) Use approximate relationships to find the electric field at a point 4.00 cm from the axis, measured radially outward from the midpoint of the shell.

Answer 1

Use Gauss's Law to calculate the net charge on the cylindrical shell based on the given electric field and radius. Apply a similar method to find the electric field at a different point close to the axis of the shell.

Step-by-step explanation:

To find the net charge on the cylindrical shell, we use Gauss's Law which states that the electric flux through a closed surface is equal to the net charge enclosed divided by the permittivity of free space (ε₀). The electric field (E) given at a distance r from the axis of the shell can be used to calculate this net charge (q) using E = q / (2πε₀rL), where r is the radial distance from the axis of the cylinder to the point where the field is being calculated, L is the length of the cylinder, and ε₀ is the permittivity of free space. Using the given E = 36.0 kN/C at a distance r = 20.1 cm and L = 2.59 m, we can rearrange this to find q.

To find the electric field at a point 4.00 cm from the axis, we can use the same approach, but now the r value will be different since the point is closer to the shell's axis. The field inside the shell would be zero if it were a closed conductor, but since it's only the curved surface that's charged, we can approximate using the field outside (just like the above method) due to the cylindrical shell's symmetry and the point being near the middle of the shell, presuming the end effects are negligible.