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**Extra info for Introductory Electromagnetics**

**Example text**

6) a function of coordinates, in general? 16. Assuming p in Eq. 8) to be known, explain in detail how you would numerically evaluate the vector integral to obtain E. 17. 16 for a surface distribution of charges over a surface S, and for a line distribution of charges along a line L. 18. Why are the formulas in Eqs. 14) only of limited practical value? 1. What would be the charge of a copper cube, 1cm on a side, if one electron were removed from all the atoms on the cube surface? 4. loz8atoms. 2.

The electric field strength at a point that is at distances r l , r2, . . 1-Superposition applied to the electric field strength. As an example, Fig. 3 shows how we obtain the electric field strength resulting from three point charges, Q, 2Q, and 3Q. Assume that the three charges are in air, in the plane of the drawing, and let us determine the total electric field at the point P which is at the same distance from the three charges. To obtain the total field, we first add up the field of the charges Q and 2Q, and then add to this sum the field of the charge 3Q, as indicated in the figure.

The inductance of a thin circular loop of radius R, made of wire of radius a, where R >> a, is given by the approximate formula 1 2 (henries), H/m, and R and a are in meters. A capacitor of capacitance C = where po = 4n 100 pF and a coil of inductance L = 100 nH are connected in series by wires of radius a and the shape of a circular loop of radius R (R >> a). 1 mm. 7. 5pF, and its resistance is R = lo6 Q. Plot the real and imaginary part of the impedance of this dominantly resistive element versus frequency from 0 MHz to 10 MHz.