Transcript Lecture-15

Magnetic Fields
Chapter 26
Last three
lectures
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
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.
This is analogous to Coulomb’s
law for the electric field of a
point charge.
At point P2 along the line of the
current element, dB due to that
element is zero.
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.