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Unformatted text preview: HW 1 Phys5406 S07 due 2/1/07
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 from knowledge of the ﬁeld.
Your answer should contain a seemingly arbitrary integration constant. However, for points
very far from the loop Φ reduces to that from only a magnetic moment term. This allows
evaluation of the integration constant; what is it? 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 . Choose the direction of the
angular velocity as the z axis. What is the magnetic moment?
3) For the case of question 2), what is B and what is the magnetic scalar potential Φ far
from the sphere? 4) An inﬁnitely long cylinder of radius R and axis along ez with permeability µ1 is completely
surrounded by material of permeability µ2 . Both permeabilities are constant. If everywhere
inside the cylinder there is a constant magnetic ﬁeld B1 = B0 ex , what is B2 and B1 · B2
at the surface of the cylinder as a function of φ, the azimuthal angle? There are no free
conduction currents anywhere. 5) A small cylinder of radius R, length L, and uniform magnetization M ex has its axis
along ex and center at the origin. A second identical coaxial cylinder is at r = −xex , where
x >> R, x >> L.
a)If the magnetizations are parallel, what force is exerted on the second cylinder?
b)If the magnetizations are antiparallel, what force is exerted on the second cylinder?
c)If the second cylinder is rotated so that the magnetizations are perpendicular, what force
is exerted on the second cylinder? 1 ...
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 Spring '10
 Blecher
 Current, Magnetism

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