The axis of a grounded cylinder of radius R is the z-axis. A line of charge...

 

Transcribed Image Text:

The axis of a grounded cylinder of radius R is the z-axis. A line of charge density is a distance d > R from the z-axis. Find the potential everywhere. Hints: (a) The distance from the line charge to the general field point r is r + d - 2rd cos 0 Chose the image charge to be X' distance d' from the origin. Find the potential o. (b) Show that if X = X', the expression for o can be simplified. (c) Show that there exists a value for d' so that is independent of 0. The key here is that at this stage, 0. (c) Add a constant to o to get the final answer. The axis of a grounded cylinder of radius R is the z-axis. A line of charge density is a distance d > R from the z-axis. Find the potential everywhere. Hints: (a) The distance from the line charge to the general field point r is r + d - 2rd cos 0 Chose the image charge to be X' distance d' from the origin. Find the potential o. (b) Show that if X = X', the expression for o can be simplified. (c) Show that there exists a value for d' so that is independent of 0. The key here is that at this stage, 0. (c) Add a constant to o to get the final answer.