Electrical ChargeHongKongPolytechnicUniversitySome Concepts:Electricalcharge（电荷)；Electricfield（电场)；Electriccurrent（电流);Conductor（导体）;Semiconductor（半导体）；Insulator（绝缘体）；Superconductor（超导体）TwoFundamentalPropertiesofElectricalCharge:Charge is quantized:Chargeis conserved:FFqiElectrostaticForce:92+kq1929192Coulomb'sLike charges repelFUnlike charges attract2Law4元0r+aFFapermittivity constant (介电常数):Note that this satisfies Newton's third lawbecause it implies that exactly the samemagnitude offorce acts onq2:Coulomb's law is a vectorequation and includes thefact that theforce acts alongthe linejoining thecharges.Like chargesrepel andunlike charges attract. Coulomb's law describes a force of infinite range which obeysthe inverse square law, and is of the same form as the gravity force.Shell Theorem:A shell of uniform charge attracts or repels a charged particle that is outside the shellas if all the shell's charge were concentrated at its center. A shell of uniform chargeexerts no electrostatic force on a charged particlethat is located insidethe shell
Hong Kong Polytechnic University Electrical Charge Some Concepts: Electrical charge (电荷); Electric field (电场); Electric current (电流); Conductor (导体); Semiconductor (半导体); Insulator (绝缘体); Superconductor (超导体); Two Fundamental Properties of Electrical Charge: Charge is quantized: ; Charge is conserved: Electrostatic Force: permittivity constant (介电常数): Note that this satisfies Newton's third law because it implies that exactly the same magnitude of force acts on q2 . Coulomb's law is a vector equation and includes the fact that the force acts along the line joining the charges. Like charges repel and unlike charges attract. Coulomb's law describes a force of infinite range which obeys the inverse square law, and is of the same form as the gravity force. Shell Theorem: A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell’s charge were concentrated at its center. A shell of uniform charge exerts no electrostatic force on a charged particle that is located inside the shell
Electrical ChargeHongKongPolytechnicUniversitySphericalConductors:If excesschargeis placed ona spherical shell thatis madeof conducting material,the excess charge spreads uniformly over the external surface.Example: The figure shows two particles fixed in a place: a particle of charge qi=+8q atthe origin of an x axis and a particle of charge q2=-2q at x=L. At what point (other thaninfinitely far away) can a proton be placed so that it is in equilibrium? Is that equilibriumstableorunstable?Solution:92Example:Thearrangementof sixfixedchargedparticles, where -30°, is shown. All six particleshave the same magnitude of charge ;theirelectricalsignsareasindicated.Whatisthenetelectrostatic force acting on qi due to the other91charges?Solution: 0
Hong Kong Polytechnic University Electrical Charge Spherical Conductors: If excess charge is placed on a spherical shell that is made of conducting material, the excess charge spreads uniformly over the external surface. Example: The figure shows two particles fixed in a place: a particle of charge q1=+8q at the origin of an x axis and a particle of charge q2=-2q at x=L. At what point (other than infinitely far away) can a proton be placed so that it is in equilibrium? Is that equilibrium stable or unstable? Solution: Example: The arrangement of six fixed charged particles, where =30 , is shown. All six particles have the same magnitude of charge q; their electrical signs are as indicated. What is the net electrostatic force acting on q1 due to the other charges? Solution: 0
Electrical ChargeHongKongPolytechnicUniversityExample: Two identical, electrically isolated conducting spheres A and B are separated bya(center-to-center)distanceathatislargecomparedtothespheres.SphereAhasapositivecharge of +Q; sphere B is electrically neutral; and initially,there is no electrostaticforcebetween the spheres. (a) Suppose the spheres are connected for a moment by a conductingwire. The wire is thin enough so that any net charge on it is negligible. What is theelectrostatic force between the spheres after the wire is removed? (b) Next, suppose sphere Ais grounded momentarily, and then the ground connection is removed. What now is theelectrostatic force between the spheres?a=0Solution:B11Q9192F(a): q= 2 = Q/2q?4元8016元80aF=0(b): qi = Q/292 = 0
Hong Kong Polytechnic University Electrical Charge Example: Two identical, electrically isolated conducting spheres A and B are separated by a (center-to-center) distance a that is large compared to the spheres. Sphere A has a positive charge of +Q; sphere B is electrically neutral; and initially, there is no electrostatic force between the spheres. (a) Suppose the spheres are connected for a moment by a conducting wire. The wire is thin enough so that any net charge on it is negligible. What is the electrostatic force between the spheres after the wire is removed? (b) Next, suppose sphere A is grounded momentarily, and then the ground connection is removed. What now is the electrostatic force between the spheres? Solution: ( ): 2 0 0 16 1 4 1 ( ): 2 1 2 2 0 2 1 2 0 1 2 b q Q q F a Q a q q a q q Q F
Electrical ChargeHongKongPolytechnicUniversityHomework:41. The figure shows two charges, qi and q2, held in afixed distance d apart. (a)What is the magnitude of thedelectrostaticforce that acts on q,?Assumethatqi=q2=20.0μC and d=1.50m. (b)A third chargeq3=20.0 μC is brought in and placed as shown in the99figure. What now is the magnitude of the electrostatic(b)(a)force on qi?2. In the basic CsCl (cesium chloride) crystal structure,Cs+ionsform the cornersof a cube and a Cl-ion is atthe cube's center.The edge length of the cube is 0.40nm.TheCs+ionsare eachdeficientby oneelectronCI(andthuseachhasachargeof+e),andtheCl-ionhasOCst0.40nmoneexcesselectron(andthushasachargeof-e).(a)What is the magnitude of the net electrostatic forceexerted onthe Cl-ion by the eight Cs+ ions at thecornersofthecube?(b)ifoneoftheCs+ionsismissing, the crystal is said tohave a defect what is themagnitude of the net electrostatic force exerted on theCl-ionbythe sevenremaining Cs+ions?
Hong Kong Polytechnic University Electrical Charge Homework: 1. The figure shows two charges, q1 and q2 , held in a fixed distance d apart. (a)What is the magnitude of the electrostatic force that acts on q1? Assume that q1=q2=20.0C and d=1.50m. (b)A third charge q3=20.0 C is brought in and placed as shown in the figure. What now is the magnitude of the electrostatic force on q1? 2. In the basic CsCl (cesium chloride) crystal structure, Cs + ions form the corners of a cube and a Cl ion is at the cube’s center. The edge length of the cube is 0.40 nm. The Cs + ions are each deficient by one electron (and thus each has a charge of +e), and the Cl ion has one excess electron (and thus has a charge of –e). (a) What is the magnitude of the net electrostatic force exerted on the Cl ion by the eight Cs + ions at the corners of the cube? (b)If one of the Cs + ions is missing, the crystal is said to have a defect; what is the magnitude of the net electrostatic force exerted on the Cl ion by the seven remaining Cs + ions?
Electric FieldsHongKongPolytechnicUniversityElectricFieldElectric field is defined as the electric force per unit charge.The direction of the fieldis taken to be the direction of the force it would exert on a positive test charge.Theelectricfieldisradially outwardfromapositive charge andradially intowardanegativepointcharge.Conversely,theelectrostatic force acting on a particlewith a chargegisElectricFieldof Point Charge:Resultant FieldElectricfieldKofchargeqElectricfieldF1yIndividual pointofchargeq2OchargefieldsareEixEresolvedintoApositivenumberistakentobeancomponentsforvectoraddition.90outwardfieldthefieldofanegativecharge is toward it. The electric fieldfrom any numberof point charges canbeobtainedfromavectorsumoftheindividual fields
Hong Kong Polytechnic University Electric Fields Electric Field Electric field is defined as the electric force per unit charge. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge. Conversely, the electrostatic force acting on a particle with a charge q is Electric Field of Point Charge: A positive number is taken to be an outward field; the field of a negative charge is toward it. The electric field from any number of point charges can be obtained from a vector sum of the individual fields