UNIT 19 : MAGNETIC FIELD

# UNIT 19 : MAGNETIC FIELD

## UNIT 19 : MAGNETIC FIELD

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1. UNIT 19 : MAGNETIC FIELD 19.1 Magnetic field 19.2 Magnetic field produced by current- carrying conductor 19.3 Force on a moving charged particle in a uniform magnetic field 19.4 Force on a current-carrying conductor in a uniform magnetic field 19.5 Forces between two parallel current- carrying conductors 19.6 Torque on a coil 19.7 Motion of charged particle in magnetic field and electric field

2. 19.1 Magnetic Field (1 hour) Learning Outcomes : At the end of this lesson, the students should be able to ; • Define magnetic field. • Identify magnetic field sources. • Sketch the magnetic field lines.

3. 19.1 Magnetic field • is defined as a region surrounding a magnet • or a conductor carrying current where a • magnetic force is experienced. • Magnets always have two poles : • a) North and south poles. • b) Like poles repel and unlike poles attract. Magnetic field lines • A magnetic field can be represented by • magnetic field lines (straight lines or curves). • Arrows on the lines show the direction of the • field : the arrows point away from north poles • and towards south poles.

4. Magnetic field lines 19.1 Magnetic field • A uniform field is represented by parallel • lines. This means that the number of lines • passing perpendicularly through unit area • at all cross-sections in a magnetic field • are the same as shown below. unit cross-sectional area

5. Magnetic field lines 19.1 Magnetic field • A non-uniform field is represented by non- • parallel lines. The number of magnetic field • lines varies at different unit cross-sections • as shown below. A1 A2

6. direction of magnetic field at point P. P Magnetic field lines 19.1 Magnetic field • Magnetic field lines do not intersect • one another. • The tangent to a curved field line at a • point indicates the direction of the • magnetic field at that point.

7. Magnetic field lines 19.1 Magnetic field • The number of lines per unit cross section • area is an indication of the “strength” of • the field. The number of lines per unit • cross-sectional areaisproportional to • the magnitude of the magnetic field. A1 A2 stronger field in A1

8. Magnetic field lines 19.1 Magnetic field • Magnetic field can also be represented by • crosses or by dotted circlesas shown • below. Magnetic field lines leave the page perpendicularly Magnetic field lines enter the page perpendicularly B into the page B out of page

9. Field Patterns 19.1 Magnetic field • The magnetic field lines pattern can be • obtained by using iron filings or a plotting • compass. the arrowhead of a compass needle is a north pole.

10. 19.1 Magnetic field Field Patterns • The direction of the magnetic field at a point • is defined as the direction of a compass • needle points when placed at that point.

11. 19.1 Magnetic field Field Patterns a. A bar magnet b. Horseshoe or U magnet c. Two bar magnets (unlike pole) - attractive

12. 19.1 Magnetic field Field Patterns d. Two bar magnets (like poles) - repulsive Neutral point (point where the resultant magnetic force/field strength is zero)

13. 19.1 Magnetic field Field Patterns e. A circular coil f. A long straight wire g. A solenoid

14. Field Patterns 19.1 Magnetic field h. Earth Magnetic Field

15. area, A 19.1 Magnetic field Magnetic Flux, Ф • is a measure of the number of field lines • that cross a surface area. • is defined as the scalar product between • the magnetic flux density, B and the vector • of the surface area, A.

16. area, A 19.1 Magnetic field Magnetic Flux, Ф • scalar quantity. • unit : weber(Wb)/ tesla-meter squared(T.m2) • 1 T.m2 = 1 Wb • Consider a uniform magnetic field B • passing through a surface area A as shown • in figure below. In Figure below,  = 0

17. 19.1 Magnetic field Magnetic Flux, Ф If  = 90 Magnetic Flux Density, B • is defined as the magnetic flux per unit • area at right angles to the magnetic field.

18. 19.1 Magnetic field Magnetic Flux Density, B • vector quantity and its direction follows the direction of the magnetic field. • unit : weber per metre squared (Wb m-2) or tesla (T).

19. 19.2 Magnetic field produced by current-carrying conductor (1 hour) Learning outcomes : At the end of this lesson, the students should be able to ; Apply magnetic field formula ; (i) for a long straight wire (ii) for a circular coil (iii) for a solenoid

20. Current out of the page 19.2 Magnetic field (B) produced by current - carrying conductor • B is a vector quantity. • Magnitude : A long straight wire (4 x 10 -7 H m-1) View from the top

21. 19.2 Magnetic field (B) produced by current - carrying conductor B = magnetic field strength / flux density (T) I = current in the wire (A) r = perpendicularly distance of P from the wire (m) μo= constant of proportionality known as the permeability of free space (vacuum) = 4πx 10-7 Henry per metre (H m-1) r P • Direction : right-hand grip rule out of the page

22. 19.2 Magnetic field (B) produced by current - carrying conductor Example 19.2.1 Determine the magnetic field strength at point X and Y from a long, straight wire carrying a current of 5 A as shown below. X 2 cm I = 5 A 6 cm Y = 5.0 x 10-5 T , into the page BY = 1.67 x 10-5 T , out of the page

23. 19.2 Magnetic field (B) produced by current - carrying conductor Exercise (DIY) 1. Two straight parallel wires are 30 cm apart and each carries a current of 20 A. Find the magnitude and direction of the magnetic field at a point in the plane of the wires that is 10 cm from one wire and 20 cm from the other if the currents are (i) in the same direction, (ii) in the opposite direction.

24. X N S 19.2 Magnetic field (B) produced by current - carrying conductor A circular coil N S

25. 19.2 Magnetic field (B) produced by current - carrying conductor A circular coil r Magnetic field strength at the center given as r = radius of the coil (m) * For N loops / number of turns on the coil

26. 19.2 Magnetic field (B) produced by current - carrying conductor Example 19.2.3 A circular coil having 400 turns of wire in air has a radius of 6 cm and is in the plane of the paper. What is the value of current must exist in the coil to produce a flux density of 2 mT at its center ?

27. or X X X X 19.2 Magnetic field (B) produced by current - carrying conductor A solenoid

28. 19.2 Magnetic field (B) produced by current - carrying conductor A solenoid Magnetic field strength at the center L = number of turns per length

29. 19.2 Magnetic field (B) produced by current - carrying conductor Example 19.2.4 An air-core solenoid with 2000 loops is 60 cm long and has a diameter of 2.0 cm. If a current of 5.0 A is sent through it, what will be the flux density within it ?

30. 19.2 Magnetic field (B) produced by current - carrying conductor Exercise 1. A solenoid is constructed by winding 400 turns of wire on a 20 cm iron core. The relative permeability of the iron is 13000. What current is required to produce a magnetic induction of 0.5 T in the center of the solenoid ?

31. 2. A student is provided with a 3.0 m long wire with a current of 0.15 A flowing through it. What is the strength of the magnetic field at the centre of the wire if the wire is bent into a circular coil of one turn ? ( B = 1.97 x 10-7 T ) 3. A circular coil has 15 turns and a diameter of 45.0 cm. If the magnetic field strength at the centre of the coil is 8.0 x 10-4 T, find the current flowing in the coil. ( I = 19.1 A ) ( µ0 = 4π x 10-7 Hm-1 )

32. 19.3 Force on a moving charged particle in a uniform magnetic field (1 hour) Learning Outcomes : At the end of this lesson, the students should be able to ; • Use force, • Describe circular motion of a charge in a uniform magnetic field. • Use relationship

33. 19.3 Force on a moving charged particle in a uniform magnetic field. • A charge qmoving with speedvat angleӨwith the direction of a uniform magnetic field of magnitudeBexperiences a magnetic force of magnitude, * Where Ө = angle between B and v * For electron , q = e.

34. negative charge 19.3 Force on a moving charged particle in a uniform magnetic field. Direction of F : • Fleming’s right hand rule : - negative charge • Fleming’s left hand rule : - positive charge positive charge Thumb – direction of Force (F) First finger – direction of Magnetic field (B) Second finger – direction of Velocity (v)

35. X X X X X X X X X X X X 19.3 Force on a moving charged particle in a uniform magnetic field. Example 19.3.1 Determine the direction of the magnetic force, exerted on a charge in each problem below. a. b. d. c.

36. 19.3 Force on a moving charged particle in a uniform magnetic field. Example 19.3.2 Determine the sign of a charge in each problem below.

37. 19.3 Force on a moving charged particle in a uniform magnetic field. Exercise 1. Calculate the magnitude of the force on a proton travelling 3.1 x 107 m s-1 in the uniform magnetic flux density of 1.6 Wb m-2,if : (i) the velocity of the proton is perpendicular to the magnetic field. (ii) the velocityof the proton makes an angle 60 with the magnetic field. (charge of the proton = +1.60 x 10-19 C)

38. 19.3 Force on a moving charged particle in a uniform magnetic field. Example 19.3.4 A charge q1 = 25.0 μC moves with a speed of 4.5 x 103 m/s perpendicularly to a uniform magnetic field. The charge experiences a magnetic force of 7.31 x 10-3 N. A second charge q2 = 5.00 μC travels at an angle of 40.0 o with respect to the same magnetic field and experiences a 1.90 x 10 -3 N force. Determine (i) The magnitude of the magnetic field and (ii) The speed of q2.

39. 19.3 Force on a moving charged particle in a uniform magnetic field. Solution 19.3.4 q1 = 25.0 μC , v1 = 4.5 x 103 m/s, Ө1= 90.0 o F1 = 7.31 x 10-3 N, q2 = 5.00 μC, Ө2 = 40.0 o, F2 = 1.90 x 10 -3 N force. (i) (ii) v2 = 9.10 x 103 m/s

40. 19.3 Force on a moving charged particle in a uniform magnetic field. Circular Motion of a Charged Particle in a Uniform Magnetic Field • Consider a charged particle moving in a uniform magnetic field with its velocity (v) perpendicularly to the magnetic field (B). • As the particle enters the region, it will experience a magnetic force (F) which the force is perpendicular to the velocity of the particle. Hence the direction of its velocity changes but the magnetic force remains perpendicular to the velocity. • This magnetic force causes the particle to move in a circle.

41. X X X X X X X X X X X X X X X X B into the page B out of the page 19.3 Force on a moving charged particle in a uniform magnetic field. Circular Motion of a Charged Particle in a Uniform Magnetic Field • The magnetic force provides the centripetal force for the particle to move in circular motion. r=? m=?

42. 19.3 Force on a moving charged particle in a uniform magnetic field. Circular Motion of a Charged Particle in a Uniform Magnetic Field • The time for one rotation (period), and and

43. 19.3 Force on a moving charged particle in a uniform magnetic field. Circular Motion of a Charged Particle in a Uniform Magnetic Field Exercise (DIY) • 1. A proton is moving with velocity 3 x 10 5 m/s • vertically across a magnetic field 0.02 T. • (mp = 1.67 x 10 -27 kg) • Calculate ; • kinetic energy of the proton • the magnetic force exerted on the proton • the radius of the circular path of the • proton. 7.52 x 10-17 J , 9.6 x 10 -16 N, 0.16 m

44. 19.3 Force on a moving charged particle in a uniform magnetic field. Circular Motion of a Charged Particle in a Uniform Magnetic Field Exercise 1. An electron is projected from left to right into a magnetic field directed into the page. The velocity of the electron is 2 x 10 6 ms-1 and the magnetic flux density of the field is 3.0 T. Find the magnitude and direction of the magnetic force on the electron. (charge of electron = 1.6 x 10-19 C) (9.6 x 10-13 N, downwards)

45. 2. A proton with a mass of 1.67 x 10-27 kg is moving in a circular orbit perpendicular to a magnetic field. The angular velocity of the proton is 1.96 x 104 rad s-1 . Determine ; (i) the period of revolution, (ii) the magnetic field strength of the field. (charge of proton = 1.6 x 10-19 C) (T = 3.2 x 10-4 s , B = 2.05 x 10-4 T)

46. 19.4 Force on a current- carrying conductor in a uniform magnetic field (1 hour) Learning Outcomes : At the end of this lesson, the students should be able to ; (i) Use force,

47. 19.4 Force on a current- carrying conductor in a uniform magnetic field • When a current-carrying conductor is placed in a magnetic field B, thus a magnetic force will act on that conductor. • The magnitude of the magnetic force exerts on the current-carrying conductor is given by • In vector form,

48. 19.4 Force on a current-carrying conductor in a uniform magnetic field. • Direction of F: Fleming’s left hand rule. Thumb – direction of Force (F) First finger – direction of Magnetic field (B) Second finger – direction of Current(I)

49. 19.4 Force on a current-carrying conductor in a uniform magnetic field. • F = 0 when Ө=0 • F is maximum when Ө=90o

50. X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X (to the right) (to the left) 19.4 Force on a current-carrying conductor in a uniform magnetic field. Example 19.4.1 Determine the direction of the magnetic force, exerted on a conductor carrying current, I in each problem below. a. b. b. a.