Magnetic Fields Chapter 26 Definition of B 26.2 The force exerted by a magnetic field Definition of B 26.3 Motion of a charged particle in a magnetic field Applications A circulating charged particle Crossed fields: discovery of the electron The cyclotron and mass spectrometer 26.4 Magnetic force on a currents Using integration The Hall effect, Hall potential Last three lectures

26.5 Sources of the Magnetic Field This lecture 26.5 Sources of the Magnetic Field The magnetic field of moving charges The magnetic field of currents

Oersted’s experiment: he showed that a compass needle is deflected by an electric current. no current current flows

Board work Biot-Savart law The magnetic field dB produced by the current element Idl is given by However, note that the direction of dB is perpendicular to both r and dl. At point P2 along the line of the current element, dB due to that element is zero. This is analogous to Coulomb’s law for the electric field of a point charge.

Magnetic field lines Magnetic field B can be represented by field lines, and as with electric field lines, the direction of the field is indicated by the direction of the field line, and the magnitude of the field is indicated by the density of lines. There are two important differences: 1. Electric field lines are in the direction of the electric force on a positive charge, but magnetic field lines are perpendicular to the magnetic force on a moving charge. 2. Electric field lines begin on positive charges and end on negative charges; magnetic field lines neither begin nor end.

Use your right hand Exercises on handout sheet

This is the geometry for calculating the magnetic field at a point on the axis of a circular current loop. EXERCISE: What is B at the centre of the loop?

More simply: The magnetic field B due to the total current in a circuit can be calculated by using the Biot-Savart law to find the field due to each element, and integrating over all current elements in the circuit.