CONDUCTOR PROPERTIES UNDER STATIC CONDITIONS LECTURE # 14 CONDUCTOR PROPERTIES UNDER STATIC CONDITIONS

OBJECTIVES To understand what happens to excess free charge in a conductor when exposed to external electric field. To list down various conductor properties that under static conditions.

MODEL E applied P dQ Conductor Point form of the continuity of current equation Point form of Ohm’s law P dQ Point form of Gauss’s law Conductor Simple partial differential equation

SOLUTION TO PARTIAL DIFFERENTIAL EQUATION At point P Charge density at t = 0 rv Relaxation time constant rv0 Initial value at P For conductor t

ANALYSIS E net = E applied – E induce +rs E induce - rs E applied + + + + + + + + E induce - - - - - - - - - - rs E applied E net = E applied – E induce Equipotential body

CONDUCTOR PROPERTIES UNDER STATIC CONDITION The net rv = 0 inside the conductor. The net E = 0 inside the conductor. The conductor is an equipotential body. Charge density rs, if present, is found only on the surface.

EXAMPLE 14.1 Find the magnitude of the electric field intensity in a sample of silver having s = 6.17 x 107 mho/m and me = 0.0056 m2/V.s if (i) the drift velocity is 1 mm/s; (ii) the current density is 107 A/m2; (iii) the sample is a cube, 3mm on a side, carrying a total current of 80 A; (iv) the sample is a cube, 3 mm on a side, having a potential difference of 0.5 mV between opposite faces.

EXAMPLE 14.2 An aluminum conductor is 1000 ft long and has a circular cross section with a diameter of 0.8 in. If there is a dc voltage of 1.2 V between the ends, find: (i) the current density; (ii) the current; (iii) the power dissipated, using your vast knowledge of circuit theory.

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