Electric forces affect only objects with chargeCharge is measured in Coulombs (C). A Coulomb is a lot of chargeCharge comes in both positive and negative amountsCharge is conserved it can neither be created nor destroyedCharge is usually denoted by q or QThere is a fundamental charge, called eAll elementary particles have charges that are simple multiples of eParticleqProtoneNeutron0Electron-eOxygen nuc.8e++2eRed dashed line means you should be able to use this on a test, but you neednt memorize itElectricityElectric FieldsElectric Charge

Charge may be at a point, on a line, on a surface, or throughout a volumeLinear charge density units C/mMultiply by lengthSurface charge density units C/m2Multiply by areaCharge density units C/m3Multiply by volumeCharge Can Be Spread Out

Concept QuestionA box of dimensions 2 cm 2 cm 1 cm has charge density = 5.0 C/cm3 throughout and linear charge density = 3.0 C/cm along one long diagonal. What is the total charge? A) 2 CB) 5 CC) 11 C D) 29 CE) None of the above5.0 C/cm32 cm1 cm2 cm 3.0 C/cm

The Nature of MatterMatter consists of positive and negative charges in very large quantitiesThere are nuclei with positive chargesSurrounded by a sea of negatively charged electronsTo charge an object, you can add some charge to the object, or remove some chargeBut normally only a very small fraction10-12 of the total charge, or lessElectric forces are what hold things togetherBut complicated by quantum mechanicsSome materials let charges move long distances, others do notNormally it is electrons that do the movingInsulators only let their charges move a very short distanceConductors allow their charges to move a very long distance

Some ways to charge objectsBy rubbing them togetherNot well understoodBy chemical reactionsThis is how batteries workBy moving conductors in a magnetic fieldGet to this in MarchBy connecting them to conductors that have charge alreadyThats how outlets workCharging by inductionBring a charge near an extended conductorCharges move in responseSeparate the conductorsRemove the charge+

Coulombs LawLike charges repel, and unlike charges attractThe force is proportional to the chargesIt depends on distanceq1q2Other ways of writing this formulaThe r-hat just tells you the direction of the forceWhen working with components, often helps to rewrite the r-hatSometimes this formula is written in terms of a quantity0 called the permittivity of free space

Concept Question+2.0 C5.0 cm2.0 C5.0 cm5.0 cm2.0 CWhat is the direction of the force on the purple charge?Up B) Down C) LeftD) Right E) None of the aboveThe separation between the purple charge and each of the other charges is identicalThe magnitude of those forces is identicalThe blue charge creates a repulsive force at 45 down and leftThe green charge creates an attractive force at 45 up and leftThe sum of these two vectors points straight left7.2 N7.2 N

Sample Problem2.0 mC1.0 m2.0 mThree charges are distributed as shown at right. Where can we place a fourth charge of magnitude 3.0 mC such that the total force on the 1.0 mC vanishes?-4.0 mC1.0 mC?3.0 mC1.16 m

Forces From Continuous ChargesIf you have a spread out charge, it is tempting to start by calculating the total chargeGenerally not the way to goThe charge of the line is easy to find, Q = LBut the distance and direction is hard to findTo deal with this problem, you have to divide it up into little segments of length dlThen calculate the charge dQ = dl for each little pieceFind the separation r for each little pieceAdd them up integrateFor a 2D object, it becomes a double integralFor a 3D object, it becomes a triple integralqdlr

The Electric FieldSuppose we have some distribution of chargesWe are about to put a small charge q0 at a point rWhat will be the force on the charge at r?q0rEvery term in the force is proportional to q0The answer will be proportional to q0Call the proportionality constant E, the electric fieldIt is assumed that the test charge q0 is small enough that the other charges dont move in responseThe electric field E is a function of r, the positionIt is a vector field, it has a direction in space everywhereThe electric field is assumed to exist even if there is no test charge q0 presentThe units for electric field are N/C

Electric Field From a Point ChargeFrom a single point charge, the electric field is easy to findqq0It points away from positive chargesIt points towards negative charges

Electric Field from Two ChargesElectric field is a vectorWe must add the vector components of the contributions of multiple charges

Electric Fields From Continuous ChargesIf you have a spread out charge, we can add up the contribution to the electric field from each partTo deal with this problem, you have to divide it up into little segments of length dlThen calculate the charge dQ = dl for each little pieceFind the separation r and the direction r-hat for each little pieceAdd them up integrateFor a 2D object, it becomes a double integralFor a 3D object, it becomes a triple integralPdlr

(y)PWhat is the electric field at the origin for a line of charge on the y-axis with linear charge density (y) = Qy2/(y2+a2) stretching from y = a to y = ?dyrDivide the charge into little segments dlBecause it is on the y-axis, dl = dyThe vector r points from the source of the electric field to the point of measurementIts magnitude is r = yIts direction is the minus-y directionSubstitute into the integralLimits of integral are y= a and y =

Pull constants out of the integralLook up the integral

Substitute limitsSample Problem

PWhat is the electric field at the point P for a line with constant linear charge density and the geometry sketched above?dxrabcDivide the line charge into little segmentsFind the charge dQ = dx for each pieceFind the separation r for each little piece

Add them up integratexLook up integralsSample Problem

Electric Field LinesElectric field lines are a good way to visualize how electric fields work They are continuous oriented lines showing the direction of the electric fieldThey start on positive charges and end on negative charges (or infinity)They never crossWhere they are close together, the field is strongThe bigger the charge, the more field lines come out

Sample ProblemSketch the field lines coming from the charges below, if q is positive+2q-2q+qLets have four lines for each unit of qEight lines coming from red, eight going into green, four coming from blueMost of the source lines from red and blue will sink into greenRemaining lines must go to infinity

Acceleration in a Constant Electric FieldIf a charged particle is in a constant electric field, it is easy to figure out what happensWe can then use all standard formulas for constant accelerationA proton accelerates from rest in a constant electric field of 100 N/C. How far must it accelerate to reach escape velocity from the Earth (11.186 km/s)?Look up the mass and charge of a protonFind the accelerationUse PHY 113 formulas to get the distanceSolve for the distance