MAGNETOSTATICS

Introduction of magnets field and its properties

1. MAGNETOSTATICS KONGUNADU COLLEGE OF ENGINEERING AND TECHNOLOGY DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING 1 Prepared by Mr.K.Karthik AP/EEE

2. Top Ten List 1. There are North Poles and South Poles. 2. Like poles repel, unlike poles attract. 3. Magnetic forces attract only magnetic materials. 4. Magnetic forces act at a distance. 5. While magnetized, temporary magnets act like permanent magnets. What We Will Learn About Magnetism 2 Prepared by Mr.K.Karthik AP/EEE

3. Top Ten continued 6. A coil of wire with an electric current flowing through it becomes a magnet. 7. Putting iron inside a current-carrying coil increases the strength of the electromagnet. 8. A changing magnetic field induces an electric current in a conductor. 3 Prepared by Mr.K.Karthik AP/EEE

4. Top Ten Continued 9. A charged particle experiences no magnetic force when moving parallel to a magnetic field, but when it is moving perpendicular to the field it experiences a force perpendicular to both the field and the direction of motion. 10. A current-carrying wire in a perpendicular magnetic field experiences a force in a direction perpendicular to both the wire and the field. 4 Prepared by Mr.K.Karthik AP/EEE

5. For Every North, There is a South Every magnet has at least one north pole and one south pole.  By convention, we say that the magnetic field lines leave the North end of a magnet and enter the South end of a magnet.  If you take a bar magnet and break it into two pieces, each piece will again have a North pole and a South pole.  If you take one of those pieces and break it into two, each of the smaller pieces will have a North pole and a South pole.  No matter how small the pieces of the magnet become, each piece will have a North pole and a South pole.  S N S N S N 5 Prepared by Mr.K.Karthik AP/EEE

6. No Monopoles Allowed It has not been shown to be possible to end up with a single North pole or a single South pole, which is a monopole ("mono" means one or single, thus one pole).  Note: Some theorists believe that magnetic monopoles may have been made in the early Universe. So far, none have been detected. S N 6 Prepared by Mr.K.Karthik AP/EEE

7. Magnets Have Magnetic Fields We will say that a moving charge sets up in the space around it a magnetic field, and it is the magnetic field which exerts a force on any other charge moving through it. Magnetic fields are vector quantities….that is, they have a magnitude and a direction! 7 Prepared by Mr.K.Karthik AP/EEE

8. Defining Magnetic Field Direction Magnetic Field vectors as written as B Direction of magnetic field at any point is defined as the direction of motion of a charged particle on which the magnetic field would not exert a force. Magnitude of the B-vector is proportional to the force acting on the moving charge, magnitude of the moving charge, the magnitude of its velocity, and the angle between v and the B-field. Unit is the Tesla or the Gauss (1 T = 10,000 G). 8 Prepared by Mr.K.Karthik AP/EEE

9. Scientists Can Be Famous, Too! Tesla 9 Prepared by Mr.K.Karthik AP/EEE

10. Famous, continued Gauss 10 Prepared by Mr.K.Karthik AP/EEE

11. The Concept of “Fields” A magnet has a ‘magnetic field’ distributed throughout the surrounding space Michael Faraday realized that ... 11 Prepared by Mr.K.Karthik AP/EEE

12. Magnetics A magnet attracts or repels another magnet – this gives us the first observable interaction in the magnetic field –it also attracts a piece of iron. It will not attract a piece of copper. Conclusion: there are different types of material in terms of their magnetic properties. Magnetic properties are governed by the permeability of the material,  [henry/meter] 12 Prepared by Mr.K.Karthik AP/EEE

13. Magnetics The strength of the magnetic field is usually given by the magnetic flux density B [tesla] The magnetic flux density is also called magnetic induction The magnetic field intensity H [ampere/meter]. The relation between the two is simple: 13 Prepared by Mr.K.Karthik AP/EEE

14. Magnetics  =4  x10  [H/m] is the permeability of vacuum  r is the relative permeability of the medium in which the relation holds,  r is given as the ratio between the permeability of the medium and that of vacuum A dimensionless quantity associated with each material in nature. Permeabilities of some useful materials are given next. 14 Prepared by Mr.K.Karthik AP/EEE

15. Magnetics Magnetic materials: Diamagnetic,  r < 1 Paramagnetic  r > 1 Ferromagnetic  r >> 1 (iron-like) The latter are often the most useful materials when working with magnetic fields. There are other types of magnetic materials (ferrites, magnetic powders, magnetic fluids, magnetic glasses, etc.) 15 Prepared by Mr.K.Karthik AP/EEE

16. Magnetization curve and permeability of ferromagnetic materials 16 Prepared by Mr.K.Karthik AP/EEE

17. Currents, fields and flux Relation between current and magnetic flux density. For a long straight wire carrying a current I and placed in a medium of permeability   r . The magnitude of the magnetic flux density is: r is the distance from the wire to the location where the field is calculated the magnetic field is a vector and has a direction (next) - field is perpendicular to I 17 Prepared by Mr.K.Karthik AP/EEE

18. Relation between current and magnetic field 18 Prepared by Mr.K.Karthik AP/EEE

19. Magnetic flux Flux is the integral of flux density over an area S: Unit of flux is the weber [ Wb ] 1 [ Wb ] = 1 [Tm 2 ] Flux relates to power and energy in the magnetic field 19 Prepared by Mr.K.Karthik AP/EEE

20. Force in the magnetic field Force in a magnetic field is based on the fact that a charge moving at a velocity v in a magnetic field B experience a force (called the Lorentz force) given as:  vB is the angle between the direction of motion and the direction of B F is perpendicular to both v and B as shown (next). 20 Prepared by Mr.K.Karthik AP/EEE

21. Relation between charge, current and force in a magnetic field 21 Prepared by Mr.K.Karthik AP/EEE

22. 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.   I 1 I 2 F 12 F 21   I 1 I 2 F 12 F 21 22 Prepared by Mr.K.Karthik AP/EEE

23. Ampere’s Law of Force (Cont’d) Experimental facts: A short current-carrying wire oriented perpendicular to a long current-carrying wire experiences no force.  I 1 F 12 = 0 I 2 23 Prepared by Mr.K.Karthik AP/EEE

24. Forces on currents For long parallel wires, the force for a length L of the wire is: F = BIL For other configuration the relation is much more complicated but force is proportional to B , I and L . A single wire carrying a current will be attracted or repelled by a permanent magnet These principles are the basis for magnetic actuation Forces can be very large since B , I and L can be controlled and can be quite large. 24 Prepared by Mr.K.Karthik AP/EEE

25. Inductance Defined as the ratio of flux and the current that produced is: Inductance is independent of current since  is current dependent All magnetic devices have an inductance but inductance is most often associated with coils 25 Prepared by Mr.K.Karthik AP/EEE

26. Inductance Two types of inductance: 1. Self inductance: the ratio of the flux produced by a circuit (a conductor or a coil) in itself and the current that produces it. Usually denoted as L ii . 2. Mutual inductance: the ratio of the flux produced by circuit i in circuit j and the current in circuit i that produced it. Denoted as M ij . A mutual inductance exists between any two circuits as long as there a magnetic field (flux) that couples the two. This coupling can be large (tightly coupled circuits) or small (loosely coupled circuits). 26 Prepared by Mr.K.Karthik AP/EEE

27. Self and mutual inductance 27 Prepared by Mr.K.Karthik AP/EEE

28. Magnetic Flux Density where the magnetic flux density at the location of d l 2 due to the current I 1 in C 1 28 Prepared by Mr.K.Karthik AP/EEE

29. Magnetic Flux Density (Cont’d) Suppose that an infinitesimal current element Id l is immersed in a region of magnetic flux density B . The current element experiences a force d F given by 29 Prepared by Mr.K.Karthik AP/EEE

30. Magnetic Flux Density (Cont’d) The total force exerted on a circuit C carrying current I that is immersed in a magnetic flux density B is given by 30 Prepared by Mr.K.Karthik AP/EEE

31. Force on a Moving Charge A moving point charge placed in a magnetic field experiences a force given by B v Q The force experienced by the point charge is in the direction into the paper. 31 Prepared by Mr.K.Karthik AP/EEE

32. The Biot-Savart Law The Biot-Savart law gives us the B -field arising at a specified point P from a given current distribution. It is a fundamental law of magnetostatics. 32 Prepared by Mr.K.Karthik AP/EEE

33. The Biot-Savart Law (Cont’d) The contribution to the B -field at a point P from a differential current element Id l ’ is given by 33 Prepared by Mr.K.Karthik AP/EEE

34. Ampere’s Circuital Law in Integral Form Ampere’s Circuital Law in integral form states that “the circulation of the magnetic flux density in free space is proportional to the total current through the surface bounding the path over which the circulation is computed.” 34 Prepared by Mr.K.Karthik AP/EEE

35. Ampere’s Circuital Law in Integral Form (Cont’d) By convention, d S is taken to be in the direction defined by the right-hand rule applied to d l . Since volume current density is the most general, we can write I encl in this way. S d l d S 35 Prepared by Mr.K.Karthik AP/EEE

36. Applying Stokes’s Theorem to Ampere’s Law  Because the above must hold for any surface S , we must have Differential form of Ampere’s Law 36 Prepared by Mr.K.Karthik AP/EEE

37. Magnetic Dipole A magnetic dipole comprises a small current carrying loop. The point charge ( charge monopole ) is the simplest source of electrostatic field. The magnetic dipole is the simplest source of magnetostatic field. There is no such thing as a magnetic monopole (at least as far as classical physics is concerned). 37 Prepared by Mr.K.Karthik AP/EEE

38. Magnetic Dipole (Cont’d) The magnetic dipole is analogous to the electric dipole. Just as the electric dipole is useful in helping us to understand the behavior of dielectric materials, so the magnetic dipole is useful in helping us to understand the behavior of magnetic materials. 38 Prepared by Mr.K.Karthik AP/EEE

39. Boundary Conditions Within a homogeneous medium, there are no abrupt changes in H or B . However, at the interface between two different media (having two different values of m ) , it is obvious that one or both of these must change abruptly. Prepared by Mr.K.Karthik AP/EEE

40. Boundary Conditions (Cont’d) The normal component of a solenoidal vector field is continuous across a material interface: The tangential component of a conservative vector field is continuous across a material interface: 40 Prepared by Mr.K.Karthik AP/EEE

41. Torque on a Current Carrying Loop The torque acting on the loop tries to align the magnetic dipole moment of the loop with the B field holds in general regardless of loop shape 41 Prepared by Mr.K.Karthik AP/EEE

42. Energy Stored in an Inductor The magnetic energy stored in an inductor is given by 42 Prepared by Mr.K.Karthik AP/EEE