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- 1 - Chapter 7. Electrod ynamics 7.1. Electromotive Force An electric curre nt is flowing when the el ectric charges are in motion. In order to sustain an electric current we ha ve to apply a force on these char ges. In most materials the cu rrent density  J is proportional to the force per unit charge:  J = s   f The constant of proportionality s is called the conductivity of the material. Instead of specifying the conductivity, it is more common to specify the resistivity r : r = 1 s For conductors the resistivity is typically 10 -8  W-m; for semiconductor it varies between 0.01 W- m and 1 W-m, and for insulators it varies between 10 5  W-m and 10 6  W -m. In most cases the force on the charges is the electromagnetic force. In that case the current density is equal to:  J = s   E + v ¥  B ( ) If the velocity of the charges is small the second term can be ignored, and the equation for  J reduces to Ohm's Law:  J = s   E Consider a wire of cross-sectional area  A and length  L . If a potential difference V is applied between the ends of the wire, it will produce an electric field inside the wire of magnitude  E = V  L The current density in the wire is therefore equal to  J = s V  L The total current flowing through the wire is therefore equal to

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