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Prof. David R. Jackson ECE Dept.

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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