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# Electric field of a wire

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University Electromagnetism:
Electric field of a charged thin wire

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### Electric field of a wire

1. 1. Electrical Field of a Long Wire © Frits F.M. de Mul
2. 2. E -field of a long wire Question : Calculate E -field in arbitrary points outside the wire. Available: A thin wire, infinitely long, carrying charge density  [C/m]
3. 3. E -field of a long wire <ul><li>Analysis and symmetry </li></ul><ul><li>Approach to solution </li></ul><ul><li>Calculations </li></ul><ul><li>Conclusions </li></ul><ul><li>Appendix: angular integration </li></ul>
4. 4. Analysis and Symmetry 1. Charge distribution:   C/m] 2. Coordinate axes: Z-axis // wire 3. Symmetry: cylinder 4. Cylinder coordinates: r, z  Z X Y e r e  e z
5. 5. Analysis, field build-up 1. XYZ-axes 2. Point P on Y-axis P 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 6. expect: E z =  E i,z = 0, to be checked !! Z Y X E i z i Q i at z i E i,y E i,z 5. all E i,x = 0 !!
6. 6. Approach to solution 1. Distributed charges 3. dQ =  .dz z Z Y X P dQ in dz at z 2. dE e r r 4. y- and z - components dE y dE z 5.
7. 7. Calculations (1) r e r y P 
8. 8. Calculations (2) r y P a similar calculation:
9. 9. Conclusions y P | E  ~ 1/ y P cylinder symmetry E
10. 10. Appendix: angular integration (1) r y P 
11. 11. Appendix: angular integration (2) integration over  from -  to  the end r y P 