Electricity& Magnetism Review of Coulomb`s Force,Magnetic Fields and Magnetic Force Lecture 22 Monday: 5 April 2004
Coulombs Law 1 q1 q2 F 4 0 r 2 1
8.99 109 Nm 2 /C 2 4 0 Direction is determined by opposites attract and like charges repel one another. Electromagnetism
fundamental force Interplay between electricity and magnetism Produces electromagnetic waves (light) Electricity Electric fields Set up by electric charges
F = qE Magnetism Magnetic fields Set up by electric currents (moving charges) Fmag= qv x B,
v parallel to B then Fmag = 0 F = Fel + Fmag = qE + qv x B Interaction Forces Between Magnets
Like poles repel, and unlike poles attract. Poles cannot be isolated. They occur only in pairs, as dipoles. Magnetic Fields Just as we found defining an electric field
useful, we will find defining a magnetic field useful. B is the symbol for the magnetic field. Magnetic field lines run from north poles to south poles.
Charges in a Magnetic Field Moving charges experience a force due to a magnetic field. FB = qv B Magnitude of FB is: FB = qvB sin where is the angle between v and B.
Direction is from the right hand rule. Another Example THE MAGNETIC FIELD B is the symbol for the magnetic field.
Magnetic field lines run from north poles to south poles. Charges in a Magnetic Field The magnetic force on a moving charge is perpendicular to the direction of the magnetic
field, and perpendicular to the direction of the velocity of the charge. If a charge moves parallel to the direction of a magnetic field, it experiences no magnetic force.
A charged particle enters a uniform magnetic field perpendicular to the field Speed doesnt change since acceleration is always perpendicular to the direction of motion. Motion stays perpendicular to the field
An Example Charges in a Magnetic Field If a charge moves perpendicular to a uniform magnetic field, it will travel in a circular path.
F ma v qvB sin qvB m r mv
r qB 2 Application
Earths magnetic field shields us from incoming charged particles. However, since Earths magnetic field goes from the south pole to the north, particles can travel parallel to the field and enter the atmosphere near the poles. The aurora is the result.
Aurora Mass Spectrometer The radius of the orbit of a charged particle depends on its mass. If we know its charge
and speed, we can determine its mass from the radius of the orbit. mv qB r , so m r
qB v Mass Spectrometer Mass Spectrometer
However, if v is not known, the system can still work, in terms of the accelerating potential V. 2qV qV mv , so v
m 1 2 2
Mass Spectrometer mv m 2qV Then, r qB qB m 2
m 2qV m2V r 2 2 2 q B m qB
2 2 qB 2 m
r 2V Frequency and Period qB
f 2 2 m 1 2 m T f
qB Angular Frequency Frequency or period of a circular orbit in a magnetic field does not depend on radius.
F ma 2 qvB q rB m r qB m qB
m Charges in a Magnetic Field Moving charges experience a force due to a magnetic field.
FB = qv B Magnitude of FB is: FB = qvB sin where is the angle between v and B. Direction is from the right hand rule. An Example