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hw1_p5406_s10

# hw1_p5406_s10 - HW 1 Phys5406 S10 due 1 In class we...

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HW 1 Phys5406 S10 due 1/28/10 1) In class we calculated 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. 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 sphere of radius R has a uniform volume charge density ρ 0 . It rotates about a di- ameter with constant angular velocity ω e z . a)What is the magnetic moment? b) Let’s specialize this problem to the proton. Assume mass M and uniform mass density. The proton is a spin 1/2 particle. If its center of mass is at rest its angular momentum along the z axis is ¯ h/ 2. Calculate the magnetic moment in units of the nuclear magneton, e ¯ h 2 M , and compare with the result in the literature.

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