Coulomb’s LawElectric FieldSlide 3Slide 4Electric Field LinesElectric Field Lines, GeneralElectric Field Lines, Positive Point ChargeElectric Field Lines, Negative Point ChargeElectric Field Lines – DipoleElectric Field Lines – Like ChargesElectric Field Lines, Unequal ChargesElectric Field Lines – Rules for DrawingRelationship Between F and EElectric Field, Vector FormMore About Electric Field DirectionSuperposition with Electric FieldsSuperposition ExampleElectric Field – Continuous Charge DistributionElectric Field – Continuous Charge Distribution, contElectric Field – Continuous Charge Distribution, equationsCharge DensitiesAmount of Charge in a Small VolumeProblem-Solving StrategyProblem-Solving Strategy, contProblem Solving Hints, finalexamplesMore examplesExample of an electric dipoleSlide 29ExampleExample – Charged Disk1Coulomb’s LawCharges:A property of matter. Positive and Negative charges, the unit of charge is Coulomb.Like sign charges repel, unlike sign charges attract.Charges conserve in a system. Conductor, insulator and ground. Force between two point charges:Force is a vector. Charge induction in conductor and in insulator.121212rrF221022141rqqrqqke2Electric FieldThe electric fieldWhy needed?Electrical forces described by Coulomb’s Law act at a distance. In Physics, interactions take place with either the two parties touching each other (! Inter !action), in the case of mechanical forces, like a car tire touches the ground, or through a medium or force carrier.In the case of electric (and magnetic) forces, the force carrier is a photon (light), but that’s beyond this course. There is a more traditional concept, the field, that provides an explanation. We encountered this concept in the gravitational force, which was explained by the gravitational field, do you still remember? When you are in an airplane flying in the Earth’s gravitational field (the influence range of the Earth’s gravitational force), it is this field that keeps you from going into the outer space. E3Electric FieldThe DefinitionSince the electric field is used to help explain the electric force, it must be defined using the electric force:testqFE•The electric field at a location is generated by source charges, not the test charge. It is there regardless one measures it with a test charge or not.•The electric field is the force a unit positive charge experiences at its location hence electric field is a vector. •The positive test charge is small enough so as not to distort the electric field around it. Source chargeTest chargeFE4Electric FieldThe graphic representation of electric field:Field from a positive charge.Field from a positive and two negative charges.Field from a negative charge.Question: why the E field points away from a + charge, but points to a – charge? A: the definition of the E field: the force on a positive unit charge.5Electric Field LinesField lines give us a means of representing the electric field pictoriallyThe electric field vector is tangent to the electric field line at each pointThe line has a direction that is the same as that of the electric field vectorThe number of lines per unit area through a surface perpendicular to the lines is proportional to the magnitude of the electric field in that regionEr6Electric Field Lines, GeneralThe density of lines through surface A is greater than through surface BThe magnitude of the electric field is greater on surface A than BThe lines at different locations point in different directionsThis indicates the field is non-uniform7Electric Field Lines, Positive Point ChargeThe field lines radiate outward in all directionsIn three dimensions, the distribution is sphericalThe lines are directed away from the source chargeA positive test charge would be repelled away from the positive source charge8Electric Field Lines, Negative Point ChargeThe field lines radiate inward in all directionsThe lines are directed toward the source chargeA positive test charge would be attracted toward the negative source charge9Electric Field Lines – Dipole The charges are equal and oppositeThe number of field lines leaving the positive charge equals the number of lines terminating on the negative charge10Electric Field Lines – Like ChargesThe charges are equal and positiveThe same number of lines leave each charge since they are equal in magnitudeAt a great distance, the field is approximately equal to that of a single charge of 2q11Electric Field Lines, Unequal ChargesThe positive charge is twice the magnitude of the negative chargeTwo lines leave the positive charge for each line that terminates on the negative chargeAt a great distance, the field would be approximately the same as that due to a single charge of +qUse the active figure to vary the charges and positions and observe the resulting electric fieldPLAYACTIVE FIGURE12Electric Field Lines – Rules for DrawingThe lines must begin on a positive charge and terminate on a negative chargeIn the case of an excess of one type of charge, some lines will begin or end infinitely far awayThe number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the chargeNo two field lines can cross Why?Remember field lines are not material objects, they are only a pictorial representation used to qualitatively describe the electric field13Relationship Between F and E This is valid for a point charge onlyFor larger objects, the field may vary over the size of the objectIf q is positive, the force and the field are in the same directionIf q is negative, the force and the field are in opposite directionseq=F Er r14Electric Field, Vector FormRemember Coulomb’s law, between the source and test charges, can be expressed as Then, the electric field will be 2ˆoe eqqkr=F rr2ˆeeoqkq r= =FE rrr15More About ElectricField Directiona) q is positive, the force is directed away from qb) The direction of the field is also away from the positive source chargec) q is negative, the force is directed toward qd) The field is also toward the negative source chargeUse the active figure to change the position of point P and observe the electric fieldPLAYACTIVE FIGURE16Superposition with Electric FieldsAt any point P, the total
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