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Lecture 11

Lecture 11 - Electrostatics

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PHYS 1070
The Great Orbax

L11 Recap: -Electrostatics - field, potential, charges -CURRENT -OHM'S LAW -RESISTANCE & RESISTIVITY SIMPLE CURRENTS - series, parallel, equivalent resistance -SG 8 -quiz #5 - FRIDAY -pretest 5-exp 7 -exp 8-electrical measurements & resistance -NEXT LECTURE-EXAM REVIEW -email suggestions to [email protected] -25 M/C - 50% of final grade REVIEW of ELECTROSTATICS Electric force from a charge q-2, felt by another charge q-1 Electric field generated by a charge q Relationship between electric forces felt by q-1 in electric field generated by q-2 Electric FIELD LNES can be drawn to give us a VECTOR MAP of the forces & fields that will interact with our positive test charge & we realize that the VECTOR NATURE of F and E need to be taken into account when SOLVING for the forces & fields at specific locations We briefly discussed the idea of work. WORK is required to move a charge within an E-FIELD -positive work required to move it against E field time + ------> + -negative work required to move it with E field time + ------> - This WORK is equal to the change in the stored PE of the charge W = (delta) PE W = k q1 q2 / K r -work done moving a charge q2 in a field generated by q1 V = k q / K r -electric potential generated by a charge q W = V q1 -relationship between work done by q1, in a potential generated by q2 Last lecture we discussed Nature's overwhelming urge to MINIMIZE its POTENTIAL ENERGY Drives many fundamental phenomena in kinematics, and is also a driving force in electrostatics We will be using this concept of minimizing potential energy to motivate the MOVEMENT of ELECTRONS! The reason that an electron moves from a NEGATIVE to a POSITIVE is to MINIMIZE its POTENTIAL ENERGY - e- ----> + That is why NEGATIVE work is done in the situation above... Conversely, POSITIVE work is required to move an e- AGAINST its natural tendency to minimize its own energy - CURRENT I = q/ t C/s = AMPERE [SI UNITS] Sometimes (like in the case of CELL WALLS) it's convenient to discuss CURRENT/AREA >called CURRENT DENSITY of FLUX I = J = I / area = q / area x t UNITS: Amps / m^2 = C / s * m^2 CONVENTION: Consider the current direction to be in the direction of flow of POSITIVE charges! Even though the ACTUAL charge carriers might be NEGATIVELY charged -Similar to our electrostatics discussion- POSITIVE TEST CHARGE PROBLEM: If the current measured in wire is 10 mA how many elementary charges pass a given point in a wire in one minute? I = q / t Flow rate = 10 mA = 10 x 10^-3 A I = 10 x 10^-3 C/s Per minute: I = 60 x 10^-2 C / min q = 1.6 x 10^-A C/charge Charge / min = 60 x 10^-2 C / min / 1.6 x 10^-16 C / charge =3.75 x 10^17 charges/min In general: Current = #ions/s x charge/ion ELECTRIC CURRENT flows like a WATER CURRENT & behaves similarly I-1 = I2 + I3 + I4 But who cares about charges moving about all willy-nilly? And Orbax, what impact could this possible have on my day to day life? WAIT! I HAVE AN IDEA! (Light bulb attached to battery) A SIMPLE CIRCUIT! -battery creates a potential difference which drives e- flow through wires -there is a uniform E field in the wires -e- within are accelerated due to F = q E Free electrons don't travel very far before they bump into something! They collide with the nuclear cores that create the lattice work of macroscopic materials As a result they lose ENERGY and VELOCITY to HEAT! (Almost as if their travel was RESISTED and almost as is that RESITANCE is related to material density, but more on that later! If an electrical circuit were analogous to a water circuit at a water park, then battery voltage would be comparable to . . . a) The rate at which water flows through the circuit •FLOW RATE - CURRENT b) The speed at which water flows through the circuit •AVERAGE OVERALL SPEED c) The distance which water flows through the circuit •LENGTH ***d) The water pressure between the top and bottom of the circuit •BATTERY VOLTAGE e) The hindrance caused by obstacles in the path of the moving water in the path of the moving water •RESISTANCE In most materials, the current THROUGH the material is proportional to the potential difference experienced ACROSS the material VOLTAGE is proportional to the CURRENT And ACTUALLY There is a relationship between V, I, R OHM'S LAW!! (Delta) V = I x R >use TRIANGLE R = RESISTANCE R has units V / I = volts / ampere = Ohm *4 We assume that the wires in a circuit are perfect conductors with no inherent resistance Therefore the only R in the circuit is the R we introduce! Special symbols represent our circuit > circuit diagram 0100090000032a0200000200a20100000000a201000026060f003a03574d46430100000000 0001003e210000000001000000180300000000000018030000010000006c0000000000000 0000000001f000000420000000000000000000000f52f0000a216000020454d460000010018 0300001200000002000000000000000000000000000000a00b0000240f0000d20000001101 000000000000000000000000000050340300682a0400160000000c000000180000000a000 0001000000000000000000000000900000010000000cd06000036030000250000000c0000 000e000080250000000c0000000e000080120000000c000000010000005200000070010000 01000000c9ffffff000000000000000000000000900100000000000004400022430061006c00 6900620072006900000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000037001c98370010000000809b37 00009937001b51fa61809b37007898370010000000e8993700649b37006c50fa61809b3700 78983700200000009f71476878983700809b370020000000ffffffff5c2b71001a724768ffffffffff ff0180ffff01805fff0180ffffffff00000100000800000008000080fa7c060100000000000000680 1000025000000372e90010000020f0502020204030204ff0200e1ffac0040090000000000000 09f01000000000000430061006c00690062007200000000007f000000409937008a2747683 0fe2869a09c3700ac9837009c2d40681f00000001000000e8983700e8983700087a3e681f00 0000109937005c2b71006476000800000000250000000c00000001000000250000000c0000 0001000000250000000c00000001000000180000000c00000000000002540000005400000 000000000000000001f000000420000000100000074cee1401263e14000000000340000000 10000004c000000040000000000000000000000cc060000350300005000000020001f00200 0000046000000280000001c0000004744494302000000ffffffffffffffffce060000370300000000 00004600000014000000080000004744494303000000250000000c0000000e00008025000 0000c0000000e0000800e0000001400000000000000100000001400000004000000030108 00050000000b0200000000050000000c02a4005c01040000002e0118001c000000fb020300 010000000000bc02000000000102022253797374656d000000003f3f3f3f000000000000000 0000000003f3f3f3f3f00040000002d010000040000002d01000004000000020101001c00000 0fb02f5ff0000000000009001000000000440002243616c6962726900000000000000000000 000000000000000000000000000000040000002d010100040000002d010100040000002d0 10100050000000902000000020d000000320a0a00000001000400000000005c01a4002000 0600040000002d010000040000002d010000030000000000 -the battery increases the POTENTIAL ENERGY of the charge by an amount qV (W=Vq) -as the charge travels through the RESISTOR it loses that energy as HEAT PROBLEM: What is the resistance of a light bulb that draws 0.5 A at 120V? R = V/I =120 / 0.5 =240 OHMS > :) RESISTANCE The resistance of a wire or any other material depends upon the MATERIAL, SIZE and SHAPE of the object! 0100090000032a0200000200a20
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