Introduction to Electromagnetism - 12

Announcements Midterm II Friday March 23 3 50-4 50 pm In class Current and Resistance Current Click to edit Master title style Click to edit Master text styles Second level Third level Fourth level Fifth level Instructor Franco Gaspari PHY 1040U (Physics for the biosciences) Introduction to Electromagnetism and Optics Lecture 12 February 27, 2007 This means we must have a net flow of charge across a hypothetical plane Instantaneous current Some important concepts We know that in a closed system charge is conserved, therefore, if we have a steady state current, the sum of the current at nodes in the circuit must be equal to zero. I0 I1 I2 Direction of the current the arrows are drawn in the direction in which a positive charge would move. Current density it is defined as It is a vector with the same direction of the electric field. A is the cross sectional area of the wire through which the current I goes. If we know , then the amount of current through an element dA is and the total current through a surface is If J is perpendicular to A, then I JA. Consider a conductor of cross-sectional area A. If n is the number of mobile charge carriers per unit volume, then the number of mobile charge carriers in the unit element is If q is the charge of each particle, then the total charge in the element is vd drift velocity. is the rate of flow of charges, -V V To understand drift velocity, consider a conductor in which the charge carriers are electrons. In reality, the electrons do not simply move in straight lines along the conductor. Drift Velocity The electric field inside a conductor in electrostatic equilibrium is zero How can we have a current (charges moving) In order to have a current, we must have a potential difference within the conductor. l To keep water running, we must spend energy to maintain the level difference (or potential difference). l l If we keep rotating the lever so to maintain the level difference the current will keep going. The mechanical pump is the analogue of a battery, power supply, voltage source. These devices provide the energy to keep an electric current going. An electric current occurs in metallic (mostly copper) wires. Resistance The resistor is used to control the electronic highway traffic and to perform tasks that require heat. Note that Since the presence of a potential difference V implies that an electric field E is established, we can say that a current density J and an electric field E are established in a conductor when a potential difference is maintained across the conductor. is called the conductivity. resistivity which is independent of Consider a segment of straight wire of cross-sectional area A and length L. RESISTIVITY property of the material. RESISTANCE property of an object. Note that the resistivity varies with temperature according to the formula is the resistivity of the material at T0. is a temperature coefficient. It can be proven that Example Resistance Thermometer The battery maintains a potential V across its own terminals a and b and across points c and d. A steady current I is produced in the circuit. If dq is the amount of charge going from a to b in a time dt, then The ( ) charge moves from a potential Va to a smaller potential Vb. The electric potential of the charge decreases by an amount POWER We define the power P as the rate of transfer P is also the rate of energy transfer from the battery to the external device. The unit of power is the Volt Ampere Watt In a resistor the energy is transferred through collisions in the form of heat (and it is consequently dissipated). Dissipation of power in a resistor. RESISTIVITY property of the material. RESISTANCE property of an object. a 10 cm c 2 cm. b 2cm V 100 V V 100 V a 10 cm b 2cm c 2 cm. m Electromotive Force (emf), Battery SI unit of emf is the volt (V J/C joule/coulomb).