Introduction to Magnetic Fields

1. Learning Objectives Book Reference : Pages 106-107 Introduction to Magnetic Fields To recap the nature of the magnetic field around a bar magnet & the Earth To understand the nature of the magnetic field around a current carrying wire To be able to calculate the magnitude & direction of the force on a current carrying wire in a magnetic field

2. Definition : A magnetic field is a force field which surrounds either a magnet or a wire carrying an electric current and will act upon, without contact, another magnet or current carrying wire Magnetic Fields : Recap 1 Plotting Compass • Like the other fields we have studied we represent magnetic fields diagrammatically using field lines or lines of magnetic flux

3. We name the ends of a magnet “the poles”. (North and & South). More correctly they should be referred to as the “North seeking pole” and “South seeking pole” Magnetic Fields : Recap 2 Like poles repel each other Unlike poles attract each other • The arrows on a magnetic field line represent the path which a “tiny free north pole” would take

4. The Earth has a magnetic field just like a giant magnet. • The geographic North pole has a South magnetic pole associated with it (Since a north seeking pole of a magnet will point towards it) The Earth’s Magnetic Field 1 Earth Dipole

5. Watch terminology!!! • At the geographic North pole there is a magnetic pole which we can refer to as “Magnetic North”. However it is a South pole! • Watch the field lines! The Earth’s Magnetic Field 2

6. Wires carrying a magnetic current produce a magnetic field Current carry conductors • “Maxwell’s corkscrew rule” can be used to establish the direction of this field. Note the current direction is the direction of “conventional current” positive to negative

7. A current carrying wire, with its associated magnetic field will experience a “motor effect” if placed (at a non-zero angle) in a magnetic field The Motor Effect • The force is perpendicular to both the current & the magnetic field

8. Experimentally, it can be shown that the size of the force due to the motor effect is related to the following : • The strength of the current • The strength of the magnetic field • The length of the wire • The angle between the field lines & current • In terms of angles, the force is greatest when the current is perpendicular to the field and zero when parallel to the field Factors Affecting the Motor Effect 1

9. The relationship between field, current and force can best be remembered using “Fleming's left hand rule” Fleming’s Left-Hand Rule • First finger (Field), seCond Finger (Current), Thumb (moTion)

10. Expressing the observations as proportionalities : • Force  Current (F  I) • Force  length of wire (F  l) (that is a lower case L) • F  Il • For a given magnetic field we can turn this into an equation where • F = BIl(assuming current is perpendicular to field) • Where B is the magnetic flux density and is the force per unit length, per unit current (N/m/A) but given the unit of Tesla (T) • (Note we can introduce a sin  term to the above equation to consider angle but it is beyond our spec Factors Affecting the Motor Effect 2

11. A straight horizontal wire of length 5m is in a uniform magnetic field which has a magnetic flux density of 120mT. The wire is perpendicular to the field lines which act due North. When the wire conducts a current of 14A from East to West calculate the magnitude and direction of the force on the wire • Using F = BIl • F = 120 x 10-3 x 14 x 5 • F = 8.4N • Vertically downwards Worked Example Current East to West Field due North

12. Problems 1 • a) 2.4x10-2N West, b) 4.5A east to west, c) 0.2T vertically down, d) 8.0x10-3 N due south