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Extra resources for Introductory Electromagnetics
The resulting magnetic force will be proportional to Ill1. We know that current elements are nothing but small domains with moving charges. Let the velocity of charges in the current element Illl be v, and the charge of individual charge carriers in the current element be Q. The force on the current element is the result of forces on individual moving charge carriers, so that the force on a single charge carrier should be expected to be proportional to Q v . Experimentally, the expression for this force is found to be of the form + + where the sign " x " implies the vector, or cross, product of two vectors (Appendix 1).
It is then connected to an uncharged capacitor of the same capacitance C by means of conductors with practically no resistance. Find the energy contained in the capacitor before connecting it to the other J CIRCUIT THEORY AND ELECTROMAGNETICS 27 capacitor, and the energy contained in the two capacitors. Can you explain the results using circuit-theory arguments? Can you explain the results at all? 6. 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 sketch of Volta's battery is shown in Fig. 5. The battery consisted of zinc and copper disks separated by leather soaked in vinegar. The chemical reactions between the vinegar and the two types of metal result in opposite charges on copper and zinc disks. These charges exert a force on freely movable electrons in a wire connecting them, resulting in electric current in the wire. Obviously, the larger these charges, the stronger the force on electrons in the wire. A quantity that is directly proportional to the charge on one of the disks is known as voltage.