1. E-field of a long wire1 Electrical Field of a Long Wire © Frits F.M. de Mul

2. E-field of a long wire2 Available: A thin wire, infinitely long, carrying charge density [C/m] Available: A thin wire, infinitely long, carrying charge density [C/m] Question: Calculate E-field in arbitrary points outside the wire. Question: Calculate E-field in arbitrary points outside the wire.

3. E-field of a long wire3 Analysis and symmetry Approach to solution Calculations Conclusions Appendix: angular integration

4. E-field of a long wire4 Analysis and Symmetry 1. Charge distribution:  C/m] 2. Coordinate axes: Z-axis // wire Z X Y 3. Symmetry: cylinder 4. Cylinder coordinates: r, z  erer ee ezez

5. E-field of a long wire5 Analysis, field build-up 1. XYZ-axes Z Y X 2. Point P on Y-axis P EiEi zizi Q i at z i 3. all Q i ’s at z i contribute E i to E in P 4. E i,x,E i,y, E i,z E i,y E i,z 5. all E i,x = 0 !! 6. expect: E z =  E i,z = 0, to be checked !!

6. E-field of a long wire6 Approach to solution z Z Y X P 1. Distributed charges dQ in dz at z 2. dE erer r 3. dQ =.dz 4. y- and z- components dE y dE z 5.

7. E-field of a long wire7 Calculations (1) r erer yPyP 

8. E-field of a long wire8 Calculations (2) r yPyP a similar calculation:

9. E-field of a long wire9 Conclusions E yPyP |E  ~ 1/y P cylinder symmetry

10. E-field of a long wire10 Appendix: angular integration (1) r yPyP 

11. E-field of a long wire11 Appendix: angular integration (2) r yPyP  integration over  from -  to  the end