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Unformatted text preview: HW 1 Phys5406 S05 due Jan. 27,05
1) In class we found the B ﬁeld on the axis of a circular loop of radius R carrying current I.
Now everywhere on the axis there is no current, so that the ﬁeld is derivable from a scalar
potential, Φ. Calculate Φ applicable for all points on the axis. For points very far from the
loop show that Φ reduces to that from only the magnetic moment term.
2) A conducting sphere of radius R has a uniform surface charge density σ . The sphere
rotates about a diameter with constant angular velocity ω . What is the magnetic moment?
3) A sphere of radius R and permeability µ1 is completely surrounded by material of permeability µ2 . Both permeabilities are constant. Put the origin at the center of the sphere.
If everywhere inside the sphere there is a constant magnetic ﬁeld B0 = B0 ez , what is the
magnitude of the ﬁeld in material 2 and What is B1 · B2 at the surface of the sphere as a
function of θ?
4) A Bohr magneton is the smallest non-zero magnetic moment of an electron due to its
orbital motion. Calculate this quantity (don’t just copy this from some handbook, try to
get it yourself). Now calculate the ratio of the magnitude of the force between two parallel Bohr magnetons to that between two parallel electric dipole moments of magnitude
e×0.1Angstrom. 1 ...
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