Introduction to Magnetism and Electromagnetism

1. Lectures 11 to 14 Magnetism and Electromagnetism Magnetic force and magnetic field strength. Biot-Savart’s law and its applications. Ampere’s law and its applications. Faraday’s law and its applications. The magnetic properties and magnetic materials.

2. Magnetic force and magnetic field strength

3. What is magnet? Permanent magnets • A magnet has two poles, a north pole and a south pole • No Magnetic monopole available in nature.

4. The magnetic forces Like poles repel each other, and unlike poles attract.

5. EARTH’S MAGNETIC FIELD • The geographic North Pole of Earth corresponds to a magnetic south pole, and the geographic South Pole of Earth corresponds to a magnetic north pole.

6. Magnetism is closely linked with electricity. Magnetic fields affect moving charges, and moving charges produce magnetic fields. Changing magnetic fields can even create electric fields. The types of the magnets 1- Permanent magnets, consist of magnetic iron or other magnetic materials. They exert forces on each other as well as on iron, nickel, cobalt and various alloys. 2- Electromagnets, consist of current-carrying coils with an iron core. Many applications exist, e.g., in alternating-current technology, in the construction of motors and generators, and in the construction of transformers

7. Electromagnets, consist of current-carrying coils with an iron core.

8. Magnetic force on a Charged Particle When a charge is placed in a magnetic field, it experiences a magnetic force if two conditions are met: • The charge must be moving. No magnetic force acts on a stationary charge. • The velocity of the moving charge must have a component that is perpendicular to the direction of the field.

9. Permanent magnet or moving charges have magnetic fields B has been used to represent the magnetic field, its direction is indicated by the direction of compass needle

10. Magnetic Force and Motion Since the magnetic field is perpendicular to the velocity, and if the magnetic force is the only force acting on a moving charge, the force will cause the charge to go in a circle: SF = ma, Fmag = q v B, and acirc = w2r = v2/r gives: q v B = mv2/r, or r = mv/qB . • If a charge moves parallel to the direction of a magnetic field, it experiences no magnetic force.

11. Magnetic force on a Charged Particle Right-Hand Rule The force       acting on a charged particle moving with velocity      through a magnetic field      is always perpendicular to      and     .

12. What are the differences of electric forces and magnetic forces? Fmag= qv x B F = qE • 1- Electric force is always parallel to the electric field direction. • 2- magnetic force is perpendicular to the magnetic field ,and perpendicular to the velocity of the moving charge. • 3- A magnetic force exists only for charges in motion. • 4-The electric force can do work on the particle. • 5- The magnetic force of a steady magnetic field does no work when displacing a charged particle. • 6- The magnetic force cannot change the kinetic energy of the charged particle.

13. Problem Solution

14. The Magnetic Fields Magnetic field, range of the action of force of a magnet, or of a current-carrying conductor, on other magnets. Magnetic field linesserve for visualization of magnetic fields, as do the electric field lines of electric fields. The direction of magnetic field lines is defined as the direction from the north pole to the south pole of the magnet. Magnetic field of a bar magnet.

15. The magnetic field

16. The Magnetic Fields Magnetic field,When a charged particle is moving through a magnetic field, however, a magnetic force acts on it. This expression is used to define the magnitude of the magnetic field as: B is the magnetic field, F is the magnetic force acts, q is the charge, moving with velocity v, and θ, is the angle between the direction of v and the direction of B.

17. Unit of the Magnetic Fields

18. Schaum's Beginning Physics II ch 6 page 165

20. Biot-Savart Law From their experimental results, Biot and Savart arrived at a mathematical expression that gives the magnetic field at some point in space in terms of the current that produces the field. The magnetic field described by the Biot–Savart law is the field due to a given current-carrying conductor.

21. Biot-Savart Law dB perpendicular to ds and to r where ds points in the direction of current I and r is the vector from the current element to P dB magnitude inversely proportional to r2 and proportional to current and magnitude ds and to the sine of θ, the angle between ds and r The constant μo in Biot-Savart is called the permeability of free space. μo = 4π 1.0E-7 T m /A Tesla meters /amp. μo = 1.2566 E-6 Wb/A m

23. Coulomb’s Law in Electrostatics and Biot-Savart Law • The Biot–Savart law is fundamental to Magnetostatics • It plays a role similar to Coulomb’s Law in Electrostatics. • The Biot-Savart Law relates Magnetic fields to • the electric currents which are their sources just as Coulomb’s Law relates electric fields to the point charges which are their sources. • The Biot-Savart Law provides a relation between • the moving charge and the magnetic field in magnetism. • It is an empirical law (formulated from the experimental observations) like the Coulomb’s law. • Both are inverse square laws.

24. Applications of Biot Savart’s Law • Magnetic Field Surrounding a Thin, Straight Conductor • Magnetic Field Due to a Curved Wire Segment

25. Biot-Savart Law permeability of free space B B

26. Magnetic Field Surrounding a Thin, Straight Conductor If the wire is very long, then

27. Magnetic Field Due to a Circular Arc of Wire Full Circle (f = 2p)

28. Ampere’s law • Oersted’s 1819 discovery about deflected compass needles demonstrates that a current-carrying conductor produces a magnetic field. (a) When no current is present in the wire, all compass needles point in the same direction (toward the Earth’s north pole). (b) When the wire carries a strong current, the compass needles deflect in a direction tangent to the circle, which is the direction of the magnetic field created by the current. (c) Circular magnetic field lines surrounding a current-carrying conductor, displayed with iron filings.

29. Ampere’s law

30. Ampere’s law Ampère's Circuital law relates the magnetic B field to its source, the electric current I. Statement of the Ampere’s law : The line integral of magnetic B-field around any closed path or loop is equal to the Permeability times the net electric current through the area enclosed by the loop.

31. Ampère’s Law A line integral of B.ds around a closed path equals m0I, where I is the total continuous current passing through any surface bounded by the closed path.

32. Applications of Ampere’s law • The Magnetic Field Created by a Long Current-Carrying Wire • Magnetic Field of a Solenoid • The Magnetic Field Created by a Toroid See in Libraray Physics for Scientists and Engineers, 6th Edn. (R.A.Serway, page 929 Ch 30

33. The Magnetic Field Created by a Long Current-Carrying Wire For r >= R For r < R

35. Applications of Ampere’s Law Magnetic Field of a Solenoidالمجال المغناطيسي الناشئ بواسطة ملف لولبي What is the solenoid? A solenoid is a long wire carrying steady current wound closely in the form of a helix. The wire is coated with insulating material so the adjacent turns are electrically insulated.

36. Magnetic Field of a Solenoid • A solenoid carrying current I, having radius a, length L, • Total number of turns N, Number of turns/unit length n = N/L • has magnetic field B. • B is independent of the length and diameter of the solenoid • & uniform over the cross-section of the solenoid

37. The Magnetic Field Created by a Toroidالمجال المغناطيسي الناشئ بواسطة ملف حلقي What is the toroid? • The toroid is a device consists of a conducting wire wrapped around a ring (a torus) made of a nonconducting material. • A device called a toroid is often used to create an almost uniform magnetic field in some enclosed area.

38. The Magnetic Field Created by a Toroid For a toroid having N closely spaced turns of wire, calculate the magnetic field in the region occupied by the torus, a distance r from the center. By symmetry, B is constant over the dashed circle and tangent to it

39. Faraday´s Law

40. Faraday´s Law

42. Faraday´s Law The emf induced, in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit.

44. Problem • A coil consists of 200 turns of wire. Each turn is a square of side 18 cm, and a uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from 0 to 0.50 T in 0.80 s, what is the induced emf in the coil? • Solution • A = (0.18 m)2 = 0.032 4 m2 . • The magnetic flux through the coil at t " 0 is zero because B = 0 at that time. • At t = 0.80 s, the magnetic flux •  = BA = (0.50 T)(0.032 4 m2) = 0.016 2 T.m2.

45. Motional emf • we considered cases in which an emf is induced in a stationary circuit placed in a magnetic field when the field changes with time. • In this section we describe what is called motional emf, • which is the emf induced in a conductor moving through a constant magnetic field. • The condition for equilibrium requires that • qE = qvB or E = vB the induced motional emf is

46. Problem

48. The magnetic properties and magnetic materials

49. Magnetite • Magnetite, a magnetic mineral made of iron oxide, has been found in bacteria and in the brains of birds. • Tiny crystals of magnetite may act like compasses and allow these organisms to sense the magnetic field of Earth.

50. Magnetism in materials • Atoms act like tiny magnets with north and south poles. When permanent magnets have their atoms aligned, we observe the magnetic forces.