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Prof. David R. Jackson ECE Dept.

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ECE 2317 Applied Electricity and Magnetism. Spring 2014. Prof. David R. Jackson ECE Dept. Notes 2. Notes prepared by the EM Group University of Houston. Statics. Definition: No time variation. In terms of frequency, f = 0 [ Hz ] .

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Prof. David R. Jackson ECE Dept.

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  1. ECE 2317 Applied Electricity and Magnetism Spring 2014 Prof. David R. Jackson ECE Dept. Notes 2 Notes prepared by the EM Group University of Houston

  2. Statics Definition: No time variation. In terms of frequency, f= 0 [Hz] The electromagnetic field splits into two independent parts: Electrostatics: (q, E) charges produce electric field Magnetostatics: (I, B) current produces magnetic field The static approximation is usually accurate for d << 0 (d is the dimension of the circuit or device).

  3. Statics (cont.) Example: f = 60 [Hz] Note: This is an exact (defined) value since 1983. 0 = c / f c = 2.99792458  108 [m/s] f = 60 [Hz] This gives: 0 = 4.9965106 [m] = 4,996.5 [km] = 3,097.8 [miles] Clearly, most circuits fall into the static-approximation category at 60 [Hz]!

  4. Statics (cont.) The following are special cases of electromagnetics at low frequency: • Circuit theory (e.g., ECE 2300) • Electronics • Power engineering • Magnetics (design of motors, generators, transformers, etc.) Examples of high-frequency systems that are not modeled by statics: • Antennas • Transmission lines • Microwaves • Optics ECE 3317

  5. Charge e Atom p proton: q= 1.602  10-19 [C] Ben Franklin chose the convention of positive and negative charges. electron: q= -1.602  10-19 [C] 1 [C] = (1 / 1.602 x10-19) protons = 6.242 x 1018 protons Ben Franklin

  6. Charge Density 1) Volume charge density v[C/m3] a) Uniform (homogeneous) volume charge density + + + + + + + + + + + + v Example: protons floating in space. V Uniform cloud of charge density Q

  7. Charge Density (cont.) b) Non-uniform (inhomogeneous) volume charge density + + + + + + + + + + + + v(x, y, z) dV Non-uniform cloud of charge density dQ Example: protons are closer together as we move to the right.

  8. Charge Density (cont.) v(x, y, z) dV dQ so Hence

  9. Charge Density (cont.) 2) Surface charge density s[C/m2] Example: protons are sprayed onto a sheet of paper. S s(x, y, z) Non-uniform sheet of surface charge density Q + + + + + + + + + + + + Non-uniform Uniform

  10. Charge Density (cont.) S s(x, y ,z) Q so Hence

  11. Charge Density (cont.) + + + + + + + + + + + + + + l l (x, y, z) Q 3) Line charge density l[C/m] Example: protons are sprayed onto a thread. Non-uniform line charge density Uniform Non-uniform

  12. Charge Density (cont.) + + + + + + + + + + + + + + l l (x, y, z) Q so Hence

  13. z v= v0=10 [C/m3] a y x Example Find: Q Note: This is a uniform charge density.

  14. Example z v = 2r [C/m3], r < a A separable integrand with fixed limits of integration. Note: This is a non-uniform (inhomogeneous) charge density. a Find: Q y x dV Separable integrand

  15. Example: Find the EquivalentSurface Charge Density for a Slab of Volume Charge Density y x z

  16. Example (cont.) Equivalent surface charge density: y x z

  17. Example (cont.) Compare:

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