21. Proprieties of electric charges Electric charge can be + or –Like charges repel one another; and unlike charges attract one anotherElectric charge is always conserved
3The 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.
4An 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.
53. 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
6The magnitude of the electric force: F=ke (|q1||q2|/r2)ke – Coulomb constantke = x109N m2/C2
74. 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
8Pb. 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
95. 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
10Rules 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
116. 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
127.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
13For 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
14Gauss’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
158. 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)
17Work –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)
19Δ 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
20Electric 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
22Electric 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
25The 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
26The 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
27Equipotential 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.
2911.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
36Electrical 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
38A 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