2 1. Proprieties of electric charges Electric charge can be + or –Like charges repel one another; and unlike charges attract one anotherElectric charge is always conserved
3 The object become charged because – charge is transferred from one object to another An object may have charge of ±e, ±2e, ±3ee = x10-19CSI unit: C (Coulomb)2 Insulators and conductorsIn conductors, electric charges move freely in response to an electric force. All other materials are called insulators (give an ex. of each)Semiconductors are between conductors and insulators.
4 An object connected to a conducting wire buried in the Earth is said to be grounded. Induction – charging of a conductorCharging an object by induction requires no contact with the object inducing the charge.
5 3. Coulomb’s LawAn electric force has the following properties:It is directing along a line joining the two particles and is inversely proportional to the square of the separation distance r, between themIt is proportional to the product of the magnitudes of the charges, |q1|and |q2|, of the 2 particlesIt is attractive if the charges are of the opposite sign, and repulsive if the charges have the same sign
6 The magnitude of the electric force: F=ke (|q1||q2|/r2)ke – Coulomb constantke = x109N m2/C2
7 4. Electric FieldThe electric field E produced by a charge Q at the location of a small “test” charge qo is defined as the electric force F exerted by Q and qo divided by the charge qo .E=F/qoE=ke (|q|/r2)Si unit : N/C
8 Pb. Strategies:1. Draw a diagram of the charges2. Identify the charge of interest3. Convert all units in SI4. Apply Coulomb’s Law5. Sum all the x- components of the resulting electric force6. Sum all the y-components of the resulting electric force7. Use Pythagorean theorem to find the magnitude and the direction of the force
9 5. Electric field lines1. The electric field E is tangent to the electric field lines at each point2. The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region
10 Rules for drawing electric field lines: -The lines for a group of point charges must begin on + charge and end on – charge- The number of lines drawn leaving a + charge or ending a – charge is proportional to the magnitude of the charge- No two field lines can cross each other
11 6. Conductors in electrostatic equilibrium When no net motion of charge occurs within a conductor, the conductor is in electrostatic equilibriumProprieties of an isolated conductor:1. the electric field is zero inside of the material2. any excess charge on an isolated conductor resides entirely on its surface3. the electric field just outside a charge conductor is perpendicular to the conductor’s surface4. On an irregularly shaped conductor , the charge accumulates at sharp points, where the radius of curvature of the surface is smallest
12 7.electric flux and Gauss’s Law The electric flux ( the number of the field lines) is proportional to the product of the electric field and surface of the areaΦE =EAΦE =EA cosθ
13 For a close surface, the flux line passing into the interior of the volume are negative, and those passing out of the interior of the volume are positive
14 Gauss’s Law:E= ke q|/r2A= 4πr2ΦE =EA=4π ke qΦE =q/ εoPermittivity of free space:εo=1/(4π ke )=8.85x10-12C2/Nm2The electric flux throughany closed surface is equalto the net charge inside thesurface divided by thepermittivity
15 8. Potential difference and electrical potential Work and potential energy:Potential energy is a scalar quantity with change to the negative of the work done by the conservative forceΔPE=Pef-Pei =- WfCoulomb force is conservativeIf imagine a small + charge placed in a uniform electric field E. As the charge moves from A to B, the work done on the charge by the electric field:W=FxΔx =q Ex (xf-xi)
17 Work –energy theoremW=q Ex Δx =ΔKEBut the work done by a conservative force can be reinterpreted as the negative of the charge in a potential energy associated with that forceΔPE of a system consisting on an object of charge q through a displacement Δx in a constant electric field E is given by:ΔPE =-WAB= -q Ex ΔxSI unit J (Joule)
19 Δ KE + ΔPE el = ΔKE +(0-ΙqΙ E d) =0 Similarly , KE equal in magnitude to the loss of gravitational potential energy:ΔKE +ΔPEg =ΔKE +(0 –mgd) =0ΔKE=mgd
20 Electric PotentialF = qEThe electric potential difference between points A and B is the charge in electric potential energy as a charge q moves from A to B, divided by the charge q: ΔV =VA-VB = ΔPE/qSI unit J/C or V (Joule/Coulomb or Volt)Electric potential is a scalar quantity
22 Electric potential created by a point charge: V=ke q/r 9.Electric potential and potential energy due to point chargesThe electric field of a point charge extends throughout space, so its electrical potential alsoElectric potential created by a point charge: V=ke q/rThe electric potential of two or more charges is obtained by applying the superposition principle: the total electric potential at some point P due to several point charges is the algebraic sum of the V due to the individual charges
25 The electric potential at all points on a charged conductor 10.Potentials and charged conductorsThe electric potential at all points on a charged conductorW= -ΔPE =-q( VB-VA)No net work is required to move a charge between two points that are at the same electric potentialAll points on the surface of a charged conductor in electrostatic equilibrium are at the same potential
26 The electric potential is a constant everywhere on the surface of a charged conductor The electric potential is constant everywhere inside a conductor and equal to the same value at the surfaceThe electron volt is defined as KE that an electron gains when accelerated through a potential difference of 1V1eV =1.6x C V =1.6x10-19 J
27 Equipotential surface is a surface on which all points are at the same potential The electric field at every point of an equipotential surface is perpendicular to the surface.
29 11.CapacitanceA capacitor- is a device used in variety of electric circuitsThe capacitance C of a capacitor is the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference between conductors (plates)C=Q/ΔVSI unit F (Farad)=C/V
36 Electrical Energy and Capacitance For a series combination of capacitors, the magnitude of the charge must be the same on all the platesΔV=Q/CeqΔV1=Q/C1; ΔV2=Q/C2; ΔV=ΔV1+ΔV2Q/C= Q/C1+Q/C21/C= 1/C1+1/C2 (series combination)Electrical Energy and Capacitance
38 A Dielectric- is an insulating material (rubber, plastic, waxed paper) If a dielectric is inserted between the plates, the voltage across the plates is reduced by a factor k (dielectric constant) to the value:ΔV =ΔV0/kC=k C0C=kε0 A/dThe maximum electric field is called dielectric strength