ELECTROMAGNETICS Linear Charges Surface Charges Ring Charges Volume Charges Professor: Viviana Vladutescu

LINEAR CHARGES

An infinite length line of charge,  L, is placed along the z-axis. We wish to find E at an arbitrary point P( , , z).

Redrawn problem in the r – z plane with field components for a charge element dQ as indicated.

Adding the field components for a second charge element dQ above the radial axis

Sketch to show where all the components come from to set up the integral.

Surface Charges

The point P is shown h above a current sheet of infinite extent occupying the x – y plane..

Infinite sheet of charge broken up into a continuous series of lines of charge.

Ring Charges

E is sought at point h on the z-axis from a ring of charge centered on the x – y plane.

dE components from a pair of charge segments dL on opposite sides of the ring.

Terms for setting up the integral.