The potential energy of a magnetic moment in an external
magnetic field is U = - ??B. U is smallest when B is parallel to ?
and largest when it is antiparallel. Since the magnetic moment of
the electron is directed opposite to its spin (because it has a
negative charge), the electron’s energy is highest when the spin is
parallel to B. The two possible energy states for the electron are
the spin up state (ms = 1212) and...
The energy E of a magnetic moment ~µ in a magnetic field B~ is E
= −~µ · B~ . Consider an isolated particle with magnetic moment ~µ.
The projection of ~µ along z can only take two values: (~µ)z = ±µB,
where µB is a constant called the Bohr magneton. i) What are the
particle energies E± corresponding to the two projections when the
particle is subject to a magnetic field B~ ≡ (0, 0, Bz) along the
z-axis...
Suppose that the magnetic dipole moment of Earth is 9.1 ×
1022 J/T. (a) If the origin of this
magnetism were a magnetized iron sphere at the center of Earth,
what would be its radius? (b) What fraction of the
volume of Earth would such a sphere occupy? The radius of Earth is
6.37 × 106 m. Assume complete alignment of the dipoles.
The density of Earth's inner core is 11 g/cm3. The
magnetic dipole moment of an iron atom...
A short bar magnet placed with its axis at 30° with a uniform external magnetic field of 0.25 T experiences a torque of magnitude equal to \( 4.5\times 10^{-2}\; J \). What is the magnitude of the magnetic moment of the magnet?
Calculate the
magnetic dipole
moment
in units
of (J/T)for an
electron having a principle quantum number
n =
3.
a) By using
quantum theory.
b)
Using Bohr
Theory.
You would like to store 9.7 J of energy in the magnetic field of
a solenoid. The solenoid has 600 circular turns of diameter 8.2 cm
distributed uniformly along its 28 cm length.
1. How much current is needed?
2. What is the magnitude of the magnetic field inside the
solenoid?
3. What is the energy density (energy/volume) inside the
solenoid?
Use the quantum particle wavefunctions for the kinetic energy
levels in a one
dimensional box to qualitatively demonstrate that the classical
probability distribution
(any value of x is equally allowed) is obtained for particles at
high temperatures.