1. Magnetism
The region round a magnet where a magnetic force is experienced is called a magnetic field.
The field around a magnet can be plotted with a small compass.
The resulting lines are known as lines of force,
The lines of force have a direction. It is the direction that a north pole would move if placed in the field.

2. S N

3. Flux density
The concentration of lines of force is a measure of the strength of a magnetic field and is known as the flux density (B)
The unit of flux density is the tesla (T).
The tesla is an extremely large unit.
The strength of the Earths magnetic field at the surface is around 10-5T

4. Region of lower flux density
Region of high flux density

5. Direction of field lines
Field lines always exist between the north and south poles of a magnet or magnets.
The convention is that field lines are drawn from north to south.
Field lines can never cross.

6. S N S N

7. Neutral points occur where the sum of the fields is zeroX
Neutral points occur where the sum of the fields is zero

8. When a bar magnet points north in the Earth’s field there are points where the Earth’s field and the field of the magnet sum to zero and form neutral points. S N
NORTH

9. THE MAGNETIC FIELD OF THE EARTH
On a large scale the Earth’s field is non uniform

10. Earth’s local magnetic field appears uniform locally
Earth’s local magnetic field appears uniform locally. This is how a compass behaves as it is moved across a lab bench
This is only the horizontal component of the field

11. There is also a dip angle θ is around 680 in the north of England
There is also a dip angle θ is around 680 in the north of England. So a compass on its side points down at this angle. θ

12. Soft iron in the Earth field
The Earth’s magnetic field is deviated by “ferromagnetic” materials like iron, nickel or cobalt
Soft iron in the Earth field

13. magnetic fields of electrical origin.
An electric current always has an associated magnetic field.
The field around a single straight wire is made up of concentric lines of force

14. The field around a straight wire
current
current
The direction of the field is
remembered
by the corkscrew rule

15. The convention for current into the paper (left) and out of the paper (right)X

16. COILS
The strength of the magnetic field is a vector quantity. In a coil the “sense” (direction) of the field lines are the same and add and the result is a field in which the lines are almost parallel in the centre.

17. Around a helical coil (solenoid) the field is startlingly similar to the field around a bar magnet.

18. The field inside a solenoid
An easy way to remember the poles of a solenoid given the direction of the current looking at each end of the coil.

19. The motor effect

20. S N S N

21. t F
Field I S N S N
thrust
Current

23. N S Vectors here add positively The current is into the page
Vectors At this side cancel

24. field N S
thrust
This combination of field’s is sometimes referred to as a “catapult field”

25. The force on a current carrying conductorS

26. Calculating the force on a conductor in a perpendicular magnetic field
Flux density B L
Force I
L is the length of the conductor within the field.
I is the current through the conductor.
F = BIL

27. Exam Question
At a certain point on the Earth’s surface the horizontal component of the magnetic field is 1.8 x 10-5 T. A straight piece of wire 2m long with a mass of 1.5 g lies on a horizontal woodn bench in an East-West direction. When a very large current flows in the wire momentarily it is just sufficient to cause the wire to lift off the surface of the bench.
State the direction of the current in the wire.
Calculate the current in the wire.
What other noticeable effect will this current produce?

28. Exam Question
At a certain point on the Earth’s surface the horizontal component of the magnetic field is 1.8 x 10-5 T. A straight piece of wire 2m long with a mass of 1.5 g lies on a horizontal woodn bench in an East-West direction. When a very large current flows in the wire momentarily it is just sufficient to cause the wire to lift off the surface of the bench.
State the direction of the current in the wire. To the East
Calculate the current in the wire. F=BIL, so I=F/BL
F= (1.5 x 10-3 x 9.81)N
I= (1.5 x 10-3 x 9.81)/(1.8x10-5 x 2)
I=410A
3. What other noticeable effect will this current produce?
The wire melts.

29. Current into the board
Field
Thrust on wire N S - +
134.95

30. There is a downward force on the conducting rod
There is a downward force on the conducting rod. It is fixed and cannot move.
By Newton’s first law there is an equal and opposite force on the magnetic “yoke” and the yoke is pulled up.
This reduces the force on the balance and the reading goes down N S - +
119.48
134.95

31. Exam Question
The magnitude of force in a current carrying conductor in a magnetic field is directly proportional to the magnitude of the current in the conductor. With the aid of a diagram, describe how you could demonstrate this in a school laboratory.

32. Diagram of a conductor perpendicular to a magnetic field (1)
Method of providing, varying and measuring d.c. current. (1)
Method of measuring variable force (eg top pan balance) (1)
For various values of current measure the force produced (1)
Plot F against I and straight line through origin (1)
F=BIL
FI
F/N
Gradient = BL
I/A

33. Defining the Tesla
The tesla is defined in terms of the moter effect of a conductor in a magnetic field.
1 N
Field 1T
Current 1 A
One tesla is the magnetic flux density of a field in which a force of
1 newton acts on a 1 metre length of a conductor which is
carrying a current of 1 ampere and is perpendicular to the field.

34. We may think of a “catapult” field at both sides.
Two current carrying wires with current in the same direction have magnetic fields in the same sense.
When they are brought close together they experience an attractive force
This is because the field vectors cancel in the area between them and the resultant force on each wire is towards the other.
We may think of a “catapult” field at both sides.

35. This is because the field vectors cancel in the area between them and the resultant force on each wire is towards the other.

36. deflecting charged particles
Electric currents are no more than flows of charged particles in conductors, so it is no surprise that magnetic fields can deflect the paths of moving charged particles. S
Thrust
Field + N
Current

37. deflecting charged particles
When negatively charged particles flow, the conventional current is in the opposite direction. S
Field - N
Current
Thrust

38. deflecting charged particles
The effect on a particle with a steady velocity is to push it in a circular path at right angles to the field. The path returns to a straight line when it emerges from the field S v - - N F
This has the implication that
Energy is not transferred by the field to the particle as the force on the particle is always at right angles to the direction of its travel. This always the case in circular motion

39. The charge on the particle is q and its mass is mv r
The force towards the centre is also given by
Because the particle is undergoing circular motion, the force towards the centre is:
B = magnetic flux density (T)
q is the charge (C) on the particle. (If the particle is an electron this symbol is written as e)
v is the velocity of the particle (ms-1)

40. Electromagnetic Induction

41. Magnetic Flux
The magnetic flux is important in understanding electromagnetic induction.
The magnetic flux (Φ) is a measure of the number of field lines passing through a region.
The unit of magnetic flux is the weber (W)
It is a vector quantity A
A uniform magnetic field has a constant density of field lines throughout
In a uniform field the number of field lines passing through the larger region B is greater than through the smaller region A. Therefore we can say that there is a greater flux through B than A B

42. Magnetic Flux Here the magnetic flux is the same in region A and B.
Sometimes a measure of magnetic flux can be misleading.

43. Magnetic Flux
Below the magnetic flux through region A is greater than through B because the density of the field lines is greater. A B

44. The relationship between B and Φ
If the magnetic field is perpendicular to a region with area A, and the flux density is B, Then the flux Φ in that region is given by:
Φ = AB

45. Moving a conducting wire in a magnetic field
If a wire is moved in a magnetic field such that field lines are cut an emf is induced between the ends of the wire
An emf is induced between the ends of the wire
An emf is NOT induced between the ends of the wire N N S S

46. The direction of the induced emfS
Direction of induced emf
motion
field
emf

47. Induced e.m.f and moving electrons
Motion of the bar A
Magnetic field
Force tends to move
electrons in this direction C
As we saw with free electrons moving in a field, they experience a force as show in the diagram
+++ ++ A
------ C
Here we see that conventional current will be driven from C to A if the circuit is complete. i.e. the direction of the emf is from C to A.

48. The direction of the induced emfS
With a closed conducting loop, the emf induced drives a current through the loop

49. Here a current is induced in the single turn coil in the same way.
If a current flows it always produces a field which opposes the motion of the coil. In this case a north pole is induced on the face of the coil being pulled towards the magnet.
This is a consequence of the law of conservation of energy. It always applies. It is known as Lenz’s law.

50. Again as a consequence of Lenz’s law
When the coil is withdrawn a south pole is produced to oppose the motion of the coil. N
Note that if a North pole had been produced instead, the coil would be repelled and the current due to induction increased. This would cause further repulsion. We would have built a perpetual motion machine! We would get energy for nothing in contravention of the law of conservation of energy.

51. Coils With More Turns A A A
Where the coil has more than one turn, the magnetic flux through the turns of the coil is called the flux linkage. A N
When a magnet moves through the coil, each turn of the coil cuts the magnetic field by the same amount.
So the flux linkage is just the
sum of flux through each turn.
If the magnet is moved with the same speed.
2 turns, → 2 x emf
3 turns → 3 x emf etc. A A

52. G A S N North pole induced at the top of the coil on approach
North pole induced at the bottom of the coil on leaving

53. V A Inducedemf/V S N Time/s
The direction of the emf is reversed as the induced poles of the coil are reversed. The bar magnet is accelerating so the rate of flux cutting is higher as the magnet leaves the coil, hence the larger amplitude of emf for a shorter time.

54. Faraday’s Law of Electromagnetic Induction
The e.m.f. induced in a coil depends on the rate of change of flux through the coil. N
The faster the flux changes the greater the e.m.f. induced

55. Faraday’s law of electromagnetic induction
The e.m.f. induced is proportional to the number of turns in the coil N N

56. Faraday’s law of electromagnetic induction
So combining these relationships
The units of the SI system combine in such a way that the constant of proportionality is 1
The expression to the right of the = sign is just the
rate of change of flux linkage

57. Faraday’s Law E is the e.m.f. Induced (V)
N is the number of turns on the coil
∆Φ is the change in flux though each turn of the coil. (Wb)
∆t is the time taken for the flux change.(s)
Note that in this equation the total change in flux linkage in the coil is N∆Φ.
Sometimes you may see this written as ∆NΦ.
It follows that 1 weber is the flux linkage in a coil if an emf of 1V falls evenly to zero in 1 second

58. Using Faraday’s Law
A coil of 200 turns and 3cm in diameter lies perpendicular to a uniform magnetic field with a flux density of 2 x10-2 T. The field falls evenly to 0T in 1s. Calculate the emf generated:.
Calculate the flux
through 1 turn of the coil
2 Now apply Faraday’s law V

59. Some effects of induction

60. The effect of a changing field on an aluminium ring
When the d.c. supply is switched on, there is a change in flux through the aluminium ring. An emf is induced in the ring with a field opposed to the coil. The ring is repelled and rises. As soon as the current is steady though the coil there is no further change in flux and the ring falls back.
d.c. supply to coil
When the circuit is broken, the flux changes again through the ring and the ring is repelled again in accordance with Lenz’s law.

61. The effect of a changing field on an aluminium ring
When the a.c. supply is switched on, there is a continuous change in flux through the aluminium ring. An emf is induced in the ring with a field opposed to the coil. This field reverses every time the field in the coil reverses.The ring continues to be repelled.
ac. supply to coil

62. Electromagnetic damping

63. Electromagnetic damping

64. Electromagnetic damping

65. Electromagnetic damping

66. BACK EMF
When the coil L is connected in series with the cell V it produces an increasing magnetic field as the current through the coil rises. This induces a “back emf” in the reverse direction to the emf produced by the cell.
The magnetic field stores energy transferred from V
When S is moved so that L is in series with R only, the back emf drives a current through R dissipating the energy stored.