Unit -3 Steady magnetic field

1. Unit -3Steady magnetic field

2. Magnetic flux & flux density, Magnetic dipole moment, Magnetization. Biot-Savart Law Magnetic field intensity evaluation due to infinite, finite and circular current carrying conductors, 6 Ampere’s law in integral and differential form., 1 Unit-3 2 5 3 Application of Ampere’s Law 4 Ampere's law of forces,

3. source of steady magnetic field Permanent magnet Direct current Electric field changing with time

4. There are two major laws governing the magnetostatic fields are: 1)Biot-Savart Law 2)Ampere's Law

5. Biot_Savart Law dH I Ѳ

7. Plane occupy line current & point H at p(x,y,z) ar r IdL I

8. H  I

9. I I B B Magnetic Field Lines:

11. Standard charge distubution +Q +Q +Q +Q +Q +Q +Q +Q +Q +Q +Q Point charge +Q +Q Sheet charge Line charge

12. Standard current distribution J = I/ds I = J dS Z dS dS y dL I x I dL dL I dY K = I/dy I = K dY Co-oxial cable Line current Surface current Diode or transistor Volume current Current carrying Wire

13. Magnetic field intensity due infinite line current Infinite Line Current Source point IdL (0,ø,z) R12 r1 Z r2 P(ƍ,ø,0) Field point

14. Magnetic Field intensity due to infinite line current

15. For problems on Line current

17. Z Line current along Z -Axis Line current az Y aΦ X aρ aΦ aρ aΦaz az=direction of line current=al aΦ = az X aρ aΦ = al X aρ az aρ

18. aΦ Z Line current along Y -Axis aρ aΦaz Y az aρ X aΦ Line current ay=direction of line current=al aΦ = aZ X aρ aΦ = ay X aρ aΦ = al X aρ = ay az aρ

19. aΦ Line current along X -Axis aρ aΦaz Line current Z az aρ Y aΦ X ax=direction of line current=al aΦ = az X aρ aΦ = ax X aρ aΦ = al X aρ aρ =ax az

20. Magnetic field intensity due to circular current carrying loop Z P(0,Ф,Z) dH r2 R12 ρ Y r1 P(ρ,Ф,0) I IdL X Ms,B.P.Harne

21. How aρcomponent cancel HZ H2 H1 dH P(0,0,Z) r2 IdL ρ Y IdL aρ I X Ms,B.P.Harne

22. How aρcomponent cancel HZ H2 H1 dH H ρ(aρ) Hρ(a ρ) P(0,0,Z) r2 IdL ρ Y IdL aρ I X Ms,B.P.Harne

23. H2 H1 Field point r r Idl Idl

24. Magnetic field due to a current loop

25. Amper’s force Law

26. Comarision Between Electric field & Magnetic field Steady Electric field Main source is point charge Force between two point charges Coulomb's law Steady Magnetic field Main source is current carrying conductor Force between two current carrying conductor(circuit) Amper’s Force law

27. Ampere’s Law of Force (Cont’d) dl1 dl2

28. Ampere’s Law of Force (Cont’d) The direction of the force established by the experimental facts can be mathematically represented by unit vector in direction of current I1 unit vector in direction of current I2 unit vector in direction of force on I2 due to I1 unit vector in direction of I2 from I1 28

29. Ampere’s Law of Force (Cont’d) The force acting on a current element I2 dl2 by a current element I1 dl1 is given by Permeability of free space m0 = 4p 10-7 F/m 29

30. Ampere’s Law of Force (Cont’d) The total force acting on a circuit C2 having a current I2 by a circuit C1 having current I1 is given by 30

31. Ampere’s Law of Force (Cont’d) The force on C1 due to C2 is equal in magnitude but opposite in direction to the force on C2 due to C1. 31

32. F21 F12 x x I1 I2  F12 F21 x 0 I1 I2 Ampere’s Law of Force (Cont’d) • Experimental facts: • Two parallel wires carrying current in the same direction attract. • Two parallel wires carrying current in the opposite directions repel. 32

33. Ampere’s Circuital Law

34. Comparison Between Electric field & Magnetic field Electric field Magnetic field Electric field of all point charge distribution Gauss’s law Magnetic field of line current Ampere's Circular Law

35. D ds (closed surface) Qenclosed

36. I B Magnetic Field Lines: dl(closed path) Ienclosed H Ms,B.P.Harne

37. Electric field Magnetic field

38. Ampere’s Circular Law: Ampere’s Circuital Law in integral form states that “the circulation of the magnetic field intensity in free space is proportional to the total current through the surface bounding the path over which the circulation is computed OR This Law states that line integral of magnetic field intensity H about any closed path is exactly equal to direct current enclosed by that path. ∫H.dL = I Ms,B.P.Harne

39. ∫H.dL = I The line integral of H around a closed path is termed the circulation of H. The direction of the circulation is chosen such that the right hand rule is satisfied. That is, with the thumb in the direction of the current, the fingers will curl in the direction of the circulation. Ms,B.P.Harne

40. Problems on ampere's circular law

41. Comparison Between Electric field & Magnetic field Application of Gauss’s Law Gauss’s Law is used to find flux coming out from any volume or charge enclosed in the closed surface For finding out Electric field intensity or flux density(E&D) due standard(Symentrical charge distribution) Point charge Line charge Sheet Charge Application of Ampere's Circular law Ampere’ circular law is used to find current coming out from any surface or closed path For finding out Magnetic field intensity (H)due standard(Symentrical current distribution) Line current Sheet current Volume current

42. Application of Amper’s Circular law Amper’ circular law is used to find current coming out from any surface or closed path For finding out Magnetic field intensity (H)due standard(Symentrical current distribution) Line current Sheet current Volume current

43. +Q

44. Electric field due to point charge

45. Z Magnetic field around current carrying conductor Y dy ay X Closed path dl H  I dzaz dzaz dy ay Ms,B.P.Harne

46. Y I dX (2,1,0) A B (5,1,0) dy dy (2,-1,0) D (5,-1,0) C Amperian closed path A -> B-> C-> D-> A X dX ay ax ay az Z az ax

48. Y I dX (2,1,0) B A (5,1,0) dy dy (2,-1,0) C (5,-1,0) D Amperian closed path A -> B-> C-> D-> A dX X Z

49. Z I dФ (2,0.1Π,3) B A (2,0.3Π,3) dZ dZ (2,0.1Π,1) C (2,0.3Π,1) D Amperian closed path A -> B-> C-> D-> A dФ Ф aФ aρ aФaz ρ ρ=2,Ф=0.1Π to 0.3Π,Z=1 to 3 az aρ

50. Comarision Between Electric field & Magnetic field Steady Electric field Symentricalcharge distrubution 1)Point charge 2)Line charge 3)Sheet charge Gauss’s Law to solve for the electric field intensity(E) much more easily than applying Coulomb’s Law Steady Magnetic field Symentricalcurrent distrubution 1)Line current 2)Sheet current 3)Volume current Ampere’s Circular Law to solve for the magnetic field intensity(H) much more easily than applying BiotSavart Law