Electricity and Magnetism

Electricity and Magnetism Course PA113 – Unit 3

UNIT 3 – Introductory Lecture • The Magnetic Field • Chapter 28 • Sources of the Magnetic Field • Chapter 29

Importance of Magnetic Fields • Practical Uses • Electric motors, Loud speakers, Navigation (Earth’s magnetic field) • In Experimental Physics • Mass spectrometers, Particle accelerators, Plasma confinement • In the Universe • Stars (e.g. the Sun), Interstellar space, Intergalactic structure, Jets

Importance of Magnetic Fields

Importance of Magnetic Fields • Units – SI Tesla (T) = (N C-1)/(m s-1) or N A-1 m -1 • 1 Gauss (G) = 10-4 T • Examples • Terrestrial B field ~ 4x10-5 T • Solenoid ~ 10-3 T • Permanent magnet ~ 10-1 T • Atomic interactions ~ 10 T • Superconducting magnet ~ 102 T • White dwarfs ~ 102 - 103 T • Neutron stars < 108 T

Ch28 – The Magnetic Field • 28-1 Force exerted by a Magnetic Field • 28-2 Motion of a point charge in a Magnetic Field • 28-3 Torques on current loops and magnets • 28-4 The Hall Effect

Vector Notation • The DOT product • The CROSS product

28-1 The Force Exerted by a Magnetic Field • Key Concept – Magnetic fields apply a force to moving charges Current element

28-1 The Force Exerted by a Magnetic Field

Representation of Magnetic Field • Like electric field, can be represented by field lines • Field direction indicated by direction of lines • Field strength indicated by density of lines • But, unlike electric field • Magnetic field lines perpendicular to force • No isolated magnetic poles, so no points in space where field lines begin or end

28-2 Motion of a Point Charge in a Magnetic Field • Key Concept – Force is perpendicular to field direction and velocity • Therefore, magnetic fields do no work on particles • There is no change in magnitude of velocity, just direction

Motion of a Point Charge in a Magnetic Field

28-2 Motion of a Point Charge in a Magnetic Field • Radius of circular orbit • Cyclotron period • Cyclotron frequency

28-3 Torques on Current Loops and Magnets • Key concept – a current loop experiences no net force in a uniform B field but does experience a torque

Magnetic dipole moment 28-3 Torques on Current Loops and Magnets

Integrate Zero at θ = 90o Potential Energy of a Magnetic Dipole in a Magnetic Field • Potential energy • Work done…..

28-4 The Hall Effect Vh = vdBw

Ch29 – Sources of the Magnetic Field • 29-1 The Magnetic Field of moving point charges • 29-2 The Magnetic Field of Currents • Biot-Savart Law • 29-3 Gauss’ Law for Magnetism • 29-4 Ampère’s Law • 29-5 Magnetism in matter

29-1The Magnetic Field of Moving Point Charges • Point charge q moving with velocity v produces a field B at point P μo= permeability of free space μo= 4 x 10-7 T·m·A-1

29-2 The Magnetic Field of Currents: The Biot-Savart Law • Key concept – current as a series of moving charges – replace qv by Idl Add each element to get total B field

Magnetic flux 29-3 Gauss’ Law for Magnetism • Key concept – The net flux of magnetic field lines through a closed surface is zero (i.e. no magnetic monopoles)

29-3 Gauss’ Law for Magnetism Electric dipole Magnetic dipole (or current loop)

29-4 Ampère’s Law • Key concept – like Gauss’ law for electric field, uses symmetry to calculate B field around a closed curve C N.B. This version assumes the currents are steady

29-5 Magnetism in Matter • Magnetization, M = m Bapp/0 • m is the magnetic susceptibility • Paramagnetic • M in same direction as B, dipoles weakly add to B field (small +ve m ) • Diamagnetic • M in opposite direction to B, dipoles weakly oppose B field (small -ve m ) • Ferromagnetic • Large +ve m, dipoles strongly add to B-field. Can result in permanent magnetic field in material.

End of lecture 1

Electricity and Magnetism Course 113 – Unit 3

UNIT 3 – Problem solving Lecture • The Magnetic Field • Chapter 28 • Sources of the Magnetic Field • Chapter 29

Problem Solving • Read the book!!!!! • Look at some examples • Try out some questions • Draw a diagram – include vector nature of the field (r and v or dl )

You must know how to… • Calculate force on a moving charge • Or current element • Understand the properties of a dipole • Torque and magnetic moment • Calculate the B field using • The Biot-Savart law • Ampère’s Law • Understand Gauss’ Law for Magnetism

29-2 Example – the Biot-Savart Law applied to a current loop

Field due to a current loop

2πR Field due to a current loop

Magnetic field lines of 2 loops

Many loops – a solenoid

The B field in a very long solenoid Can use the Biot-Savart Law or Ampère’s Law Length L N turns n = N/L Radius R Current I di=nIdx Field in a very long solenoid: B =0nI

Field around and inside a wire Classic example of the use of Ampère’s Law

Direction of field around a wire

End of lecture 2

Electricity and Magnetism Course 113 – Unit 3

UNIT 3 – Follow-up Lecture • The Magnetic Field • Chapter 28 • Sources of the Magnetic Field • Chapter 29