Download P114 Lecture 8

P114
Lecture 8
Douglas Cline 2014
Summary of electric currents
P114
• Permanent magnetism
• Electromagnetism
• Lorentz force
• Units
• Motion of point charges in a magnetic field
• Magnetic forces on electric currents
• Force on a current loop
Lecture 8
Permanent magnetism
• Permanent magnetism known for over 2000 years
• Magnets behave like electric dipoles in some respects.
• The same polarity magnetic poles repel and opposite polarity poles attract
• Field lines are continuous, cannot isolate an isolated magnetic monopole.
• B is the symbol used to designate magnetic field
• One end named north pole because it seeks the earth’s north magnetic pole
• Used as a magnetic compass since the twelfth century
Earth’s magnetic field
• Note confusion as to naming of
magnetic and geographic poles
• The Earth has a south magnetic pole
buried deeply under Canada about 1100
miles from the geographic north pole. The
magnetic axis is 110 from the rotation axis
of the earth
• In Rochester the north-seeking magnetic
compass needle points 11.60 west of north
geographic meridian and dips downwards
70.140. The magnetic declination has
moved 2.40 westward since 1965.
Electromagnetism
• In 1819 Hans Christian Oersted discovered that an electric current
produces a magnetic field that circles clockwise around the current
Electromagnetism
• Electric current loop produces a magnetic field similar to that from
a permanent magnet
• The lines of magnetic field are continuous.
Cross product or Vector product
The cross product vector C
AxB=C
has a magnitude given by C = |AB sinθ|
The vector C is perpendicular to the plane containing A and B
In a right-handed coordinate system the vector product can be evaluated by using
the fact that i x j = k, j x k = i, k x i = j.
Magnetic force on moving charge
• The magnetic force on a moving charge in a magnetic field B is
• The magnetic force is mutual perpendicular to both B and v
• The direction is given by the right-hand rule
Right-hand rule for direction of force
Lorentz force
The total electromagnetic force on a charge in electric field E
plus a magnetic field B is the superposition of the two forces
The E and B fields must be defined in the same frame of
reference as will be discussed later when studying the Theory of
Relativity
Is the magnetic force conservative?
Units of magnetic field B
Moving charges in a uniform B field
Cyclotron
• Maximum kinetic energy given by maximum radius
Maximum kinetic energy
• Invented 1932 by Lawrence and Livingston
• Rochester 27” Cyclotron 1934 [10.5 MeV protons and alphas]
• Rochester 130” Cyclotron 1947 [240MeV protons]
• Cyclotrons used extensively in nuclear physics and nuclear medicine
Magnetic confinement
Magnetic confinement
Magnetic bottle:
Van Allen radiation belts around
the earth:
Discovery of the electron
• J.J. Thomson (1897) measurement of e/m of electron gave single-valued quantity
• Adjust E and B such that the net Lorentz force is zero, i.e. E = v x B
• Velocity given by incident kinetic energy ½mv2 = eV
• Thus the ratio
e/m = E2/2VB2
• Millikan measured the charge e, determining both e and m of the electron
Hall Effect
Positive charge carriers
Negative charge carriers
Voltage difference across the width w of the conductor of thickness d is
V = (1/nq)(IB/d)
where nq gives the sign and magnitude of the charge carrier density.
[See lecture notes]
Magnetic force on electric currents
Magnetic force on electric currents
Magnetic torque on a current loop
Galvanometer
Summary
Lorentz force: