Question

10. A circular cylinder with a radius R of 1 cm and a height H of 2 cm carries a charge density of ρV = H r2 sin φ µC/cm3 (r is a point on the z-axis, φ is an azimuthal angle). The cylinder is then placed on the xy plane with its axis the same as the z-axis. Find the electric field intensity E and the electric potential V on point A on z-axis 2 cm from the top of the cylinder.

Answer 1

First of all divide the cylinder into infinite small discs each carrying some charge. Then take one of the discs and calculate the potential of the point with respect to that disc and then integrate the potential of all the discs in the cylinder. That way you will have the potential at that point. Now, the derivative of the potential will give you the electric field at that point. I have taken the midpoint of the cylinder as the center and hence the distance +L/2 and -L/2.

Key:-

L - length of the cylinder

Z - Distance between the center of the cylinder and the point where potential has to be found out.

R - Radius of the cylinder.

I have shown all the formulas in the images just put in the values to get the answer.

If you have any doubts or not able to read any equations just leave a comment and i will try to get a better photo of that equation.