The magnetic force on a moving charge is perpendicular to
the velocity => the acceleration is perpendicaular to the
velocity => the magnetic force tends to bend the trajectory
of the charge.
If the magnetic field is uniform, then the charge will move
in circular motion.
Trajectory calculation
Principle: F = ma
F is the force due to the magnetic field F=qvB
a is the centripetal acceleration: v**2/r, see Eq. 24-6.
If B is uniform then r =constant => the trajectory is
a circle. (If there is a velocity component along the B-field
direction, then the trajectory is a spiral).
Use trajectories to identify charge of the particle: Positive
charges bend one way and negative charges bend the other way.
Can you identify the charge of a particle by looking at their
trajectories (or tracks in a cloud chamber).
Question: Two charge particles (same charge), one's mass
is larger. Assuming they have the same speed, whose track has
a larger radius?
Question: Two charge particles (same charge), one's mass
is larger. Assuming they have the same kinetic energy, whose
track has a larger radius? Can you think of an experiemental
setup where both charge particles have the same kinetic energy?
(See the section on Mass Spectrometer on P. 794).
-> Do Problem 24-8, 24-9, P. 807.
Applications:
Mass spectrometer: Two isotopes of the same element
can be ionized to the same charge state and accelerated by a
potential difference. The heavier mass has a trajectory with
large radius, Eq. 24-12. Note: m and r are NOT linearly proportional.
Magetic bottle: Use non-uniform B-fields.
Velocity Selector: Use both B and E-field. Concept: Forces
due to E and B-field cancel each other.
Do Problem 24-11, P. 807.
Similar effect: Hall effect
Thomson's Measurement of q/m for an electron.
Cyclotron: The charge particle is accelerated the E-field
(the two voltage plates) and the motion is confined by the B-field.
Do Problem 24-16, P. 807
Torque on current loop
Eq. 24-15.
New term: magnetic dipole moment (as compared to electric
dipole moment), Eq. 24-14.
Eq. 24-15 => the magnet dipole moment tends to align with
the mgnetic field
You can think of a current loop act as like a tiny magnet
with the magnetic dipole moment point out of the north pole.