8.022pset7 - ~ A inside and outside of an inFnite solenoid...

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Massachusetts Institute of Technology Department of Physics 8.022 Spring 2004 Assignment 7: Magnetic fields and Induction Post date: Thursday, April 1st Due date: Thursday, April 8th Be sure to write your name and section number on your pset Please staple multiple pages together 1. Purcell 6.4: Practice with B-S law (5 pts). 2. Purcell 6.13: Helmholtz coil (10 pts). A Helmholtz coil was used in lecture to produce a nearly uniform ~ B field to show electrons traveling in a circle. 3. Purcell 6.16: Wire with hollow drilled out (10 pts). Hint: this is the magnetic analog of Purcell 1.16. 4. Purcell 6.17: Finite solenoids, infinite solenoids, and superposition (20 pts). Ignore the “What else can you find out?” in part (d) ... I have no idea what Purcell is going for here. 5. Purcell 6.18: Rotating charged cylinders (10 pts). 6. Purcell 6.22: Magnetic moments (15 pts). 7. Vector potential of a solenoid (10 pts): Find the vector potential
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Unformatted text preview: ~ A inside and outside of an inFnite solenoid of radius R with n turns per centimeter, each carrying current I . ±ind the solenoid which is symmetric about the axis of the solenoid. HINT : You can come up with a very simple way to compute ~ A by putting together • The magnetic ²ux, Φ B = R ~ B · d~a • The deFnition ~ B = ~ ∇ × ~ A • Stoke’s theorem. 8. Purcell 7.14: Crossbar sliding in magnetic Feld (20 pts). I don’t like Purcell’s subparts, so please do the following: (a) Write down a di³erential equation of the form dv/dt = something that governs the motion of the sliding crossbar. (b) Integrate this to Fnd the velocity v ( t ) for all t > 0. (c) Compute the total distance that the cross bar moves. (d) Show that the total energy dissipated in the resistor makes sense given the initial velocity of the crossbar....
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