Behaviour of Conductors in Electric field.pptx

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1. Behaviour of Conductors in Electric field Conductors: Depending on the response to the electric field materials can be classified as 1.Conductors 2.Semi conductors and 3.Insulators In conductors free electrons are available to carry current. Valancy band and conduction bands are overlapped Valancy electrons are easily detachable in conductors. In insulators electrons are strongly bounded to neucleus.Ordinary electric field cannot detach electrons .Hence they do not conduct

2. Insulators In insulators there is large gap between valancy and conduction bands Resistance is very high Ex:glass,wood,mica,forcelean Semiconductors: The gap between valancy & conduction band is less By adding impurities(doping) we can make them to conduct Ex:silicon,germanium

3. Behaviour of conductor in electric field

4. Free electrons in the conductor move in the opposite direction of E - ve charge will occur when the flux lines entre and + ve charge will occur when the flux lines leave. Charge density inside the conductor is Zero Charge accumulated at the surface of the conductor. The flux lines on the surface is perpendicular to conductor surface

5. Conductor placed in an Electric field E behaves Electric field intensity inside the conductor body is zero because internal field is equal and opposite of external field. Charges are distributed outside the conductor surface. Electric flux lines leave or enter at 90 degrees to the surface. In conductors electrons move freely under the influence of the field. Potential on the surface & inside the conductor is same every where. Hence the conductor surface is a equipotential region. Hence ▼V=-E=0 throughout the body of conductor. No charge is enclosed inside the conductor body since all charges are on the surface i.e charge resides on the surface and not inside

6. Relaxation Time If some change is placed suddenly on a body a finite time is required for redistribution of flux lines.This time delay is called relaxation time For good conductors 10 -19 sec For insulators 10 6 sec So relaxation time is very very small for conductors and very large for insulators

7. Relation b/n P and E: q- charge on the plate - induced charge due to dielectric. Due to induced charge there is internal field which opposes the external field . Polarisation – P = dipole moment/unit volume Volume = A x l (Area of the slab =l) P = = = P - charge /area same as units of D . Without dielectric = E E- external field. With dielectric D = E Polarisation is the difference of D and  

8. P= D-D0 =EƐ0Ɛr-EƐ0=EƐ0(Ɛr-1) P=Ɛ0XeE Xe = (Ɛr-1) Electric susceptibility of the di electric medium P= D-D0= EƐ0(Ɛr-1) P=Polarisation=induced dipole moment per unit volume P=q1/A, q1-induced charge D= EƐ0 with no dielectric With dielectric D= EƐ0+p P proportional to E, p= Ɛ0XeE D= EƐ0+p= EƐ0+Ɛ0XeE=Ɛ0(1+Xe)E We know that D=EƐ0Ɛr Comparing Ɛr =1+Xe

9. D = E = E + P With dielectric D= P = ( -1 ) E E = , E = effect of dielectric is taken as P = D E = = = q D is independent dielectric  

10. Properties of dielectric: 1.Dielectricities do not contain any free charges .They contain only bound charges since no current flow. 2.When subjected external field E bound charges drift their relative positions. Small dipoles are induced .That is there is a induced charge q 1.This is called polarisation. 3.Due to polarisation dipoles can store energy. 4.Flux density is increased due to polarisation D = E + P. 5.Induced dipoles produce electric field E i which opposes the external field. 6.Due to induced charged q 1 volume charge density is formed inside dielectric.The surface charge density due to q is formed on the surface . 7.Electric field inside the dielectric gets modified by the polarization  

11. Polarisation in dielectrics When a dielectric slab is placed in an electric field E e (say between two charged plates of a capacitor).

12. The centre of gravity of + ve charge of dielectric are pulled towards – ve plate of capacitor and centre of – ve charge s in dielectric are pulled to + ve plate of capacitor. Thus + ve & - ve charges are formed on the surface of the dielectric . The remaining – ve & + ve charges in the middle of dielectric gets neutralized leaving + ve charges near – ve plate and – ve charges near + ve plate . The net effect of electric field applied is to form a layer of + ve & - ve charges near the surface of dielectric. These charges are called induced charges. The induced charges in dielectric set up an internal field opposite to applied field inside the slab. This effect is known as polarisation of dielectric.  

13. Polarisation & charge density: When a dielectric slab is placed in an electric field ,orientation of charges takes place and dipoles are formed.(induced) The electric dipole moment per unit volume is called POLARISATION . ------- Polarisation vector. ----- External field perpendicular to the force of dielectric ADGH. E ------- Internal field due to induced charges in BCEF (surface + )and ADGH surface (- ve ) due to the induced or bound charges . These bound charges disappear when field is withdrawn.  

14. Charge density of induced charges: Let A be area of dielectric slab of BCEF & ADGH faces. l- height of the slab. Let +q be induced charge BCEF face -q be induced charge ADGH face. Dipolemoment P of induced charge P = l The volume of the slab Al Polarisation P = = = C/ Polarisation =P = induced surface charge density. Hence polarization = surface charge density of induced charge.  

15. Dielectric materials : 1. Non-polar 2. Polar types Non polar dielectric :(no permanent dipoles) In this centres of – ve & + ve charges coincide each other and hence dipole moment = 0 When there is no electric field = 0 When electric field is applied there is a displacement between centres of + ve and – ve charge and hence constitute dipoles . Hence dipoles are induced in dielectric due to electric field. These induced dipoles produce electric field in the opposite direction of electric field applied. P = dipoles/ unit volume.  

16. Polar dielectric : There is a permanent dipole formation in atoms/molecules of dielectric material. When field applied = 0 ,the permanent dipoles are randomly oriented giving average dipole moment = 0. When external field is applied ,partial alignment of dipoles take place in the direction of . The alignment is never perfect ,they are in always thermal agitation . Allignment of dipoles increases with field strength. Total dipolemoment in the dielecgric p = P α E ; P = E = due to permanent dipole moment. = due to induced dipole moment  

17. Dielectric constant: = K = = K = = = = = = = K = = C --- increases with dielectric V --- between plates decrease with dielectric When dielectric is placed in a dielectric E it is polarised (P) P α E P = E ----- electric susceptibility = =  

18. Gauss law in dielectric : D .ds = Q = Ѱ = ꭍ E.ds = Q ꭍ E.ds = Ѱ = ꭍ E.ds = Electric flux lines = Q ꭍ .ds = = A = Electric flux coming out of the closed surface is 1/ times the charge enclosed = = Ѱ When no dielectric is present = ꭍ .ds = ꭍ ds = A A = area of the plate. D = A = = with = 1  

19. (2) When dielectric is placed between the plates: PQRS ------ gaussian surface Netcharge with in PQRS = q- E = resultant field in the dielectric ꭍ E.ds = = = EA E = = - = - E is less than By definition K = = E = = - = ( = - ) Therefore = q - = q  

20. ꭍ E ds = Or K ꭍ E ds = = EAK or ꭍ E ds = E =  

21. Relation between Electric field Intensity E Dielectric Polarization P, Flux Density D When a dielectric slab is placed in a parallel plate condenser with charge ‘q’ -The dielectric medium is polarized(p) -Induced charges appear on the dielectric surface –q 1 - Electric field is set up inside the dielectric E i ( opposite to that of applied E ) q-charge on plate, q1-induced charges D-independent of dielectric E = = -  

22. = + = [ + ]= [ ]+ =D flux density, =P =E electric field in the dielectric D= E+P= [ ]+ P=D- E  

23. D and P in terms of E : E= = = D = E = is called permittivity of the medium. K= = (relative permittivity) D = E +P = E ; = +1 P = D- E P= K E - E = E (K-1) We know that Pα E P= E E = E (K-1) = K - = - = ( -1) = ( -1) = K - K = 1+  

24. Dielectric boundary conditions Flux lines in a dielectric are continuous Flux lines get refracted when passing from medium 1 to medium 2 of different Boundary conditions for D&E:  

25. The normal component of D is same on both sides boundary Dn1=Dn2 i.e normal component of D is continuous. No deviation Tangential component of E on the boundary are equal Et1=Et2 PROOF : Consider a small pill box with ‘ds ‘ area of top and height Δ h ꭍ (Gauss Law) Let Dn1=Dn2 are normal components of D Since Δ h is very small all flux is coming out from ds Dn1.ds =Dn2.ds=q Since the charge on the boundary =0 (boundary free from charge q=0 dielectric) q=0 cos = cos -----------(1)  

26. Trangential component of E: Consider a rectangle ABCD = As Δh → 0 , 0 = dl -ꭍ dl =0 dl - dl = 0 = = sin = sin ------------(2) Dividing 2 by 1 = = and =  

27. tan = tan = = Boundary conditions are = ; = ; =  

28. CAPACITOR & CAPACITANCE Capacitor : has two conducting surfaces separated by d and filled with dielectric. Capacitance : property of capacitor is to store energy in electric field and is called the capacitance. C → defined amount of charge required to create P.D of one volt Q = CV C = 1 farad = 1C/volt C = 1F if Q = 1C and V = 1V.  

29. Capacitance of an isolated sphere : Consider a sphere of radius r having a charge q. Assume second sphere of ꝏ radius and zero potential. Flux density D = E = = Work done = -q ꭍ E.dl V = voltage = = - ꭍ E.dl V = - dr = - V = C = C = = therefore C = 4 П  

30. Capacitance of spherical capacitor : V = - dr = C = = C = 4 П Capacitance of a parallel plate capacitor: Let A be the area of the plate q- charge D = ; E = = ; E = ; V = Ed = d ; V = = C = for air =  

31. Capacitance of a parallel plate capacitor with composite dielectric: Let the charge density on the plate = σ C/ D = σ = A = area of plate Total voltage V = = = = = = V = + since V = Ed = C = = With ‘n’ dielectrics in between plates C = =  

32. Energy stored in a capacitor: At a given instant Let q be the charge transferred to plate by the voltage V C= ; V = Now let be the charge raised on the plate Workdone for this dw = V d V = dw = V. dq = dq Total workdone to transfer total charge Q W = . dq = W = Q = V Q = If there are n charges ----- W = Workdone if the charge is distributed uniformly in a volume with volume density W = .V dv  

33. CONVECTION CURRENT: The current that flows in gas or free space(current through non-conductor medium ex;cro ) = Charge density/unit volume drift velocity of charge particles in m/sec As charges pass through a surface S persec .It constitutes the convection current J= . vd where , vd may not be constant. Conduction Current Density: Conduction current is flow of electrons in Conductor of fixed area. J= . = µE Drift velocity ꝏ E µE  

34. µ → electrons mobility J = ( . µ) E = σ E J = σ E σ→ conductivity of the material J = σ E point form of ohms law (valid for all types of current )  

35. Equation of Continuity Relating current density ------J And charge density------- This equation is based on the conservation of the charge ; ; Q= , ; q=  

36. = =- As per the divergence theorem = =- =- =0 ,integral is zero only if =0 This is called equation of continuity or Maxwell’s equation  

37. Ohms law in point form I= = = = . E = = J = = E. σ I = ; = J = = E. σ J= E. σ ; σ = point form of ohmslaw .