hw3_p5406_s07

# hw3_p5406_s07 - U = R as dV A Â J Show that the change in...

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HW 3 Phys5406 S07 due 2/8/07 1)JDJ 4-13 2)A uncharged, conducting sphere of mass M and radius R ﬂoats with 1/4 of its volume submerged in a dielectric liquid of permitivity ± . When a total free charge Q is put on the sphere it ﬂoats with 1/2 its volume submerged. Calculate, the Q = f ( ±, R, M ) needed. 3) Suppose a conducting sphere of radius R is cut through a diameter into two hemispheres. The hemispheres are glued together and a charge Q is placed on the sphere. How much force must the glue withstand to keep the hemispheres from pulling apart. 4)Start with the expression for the magnetic potential energy for a non-linear system,
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Unformatted text preview: U = R as dV A Â· J . Show that the change in energy Î´U for a small change in J is, Î´U = Z as dV B Â· Î´ H . 5) Suppose a long solenoid of n turns/length, radius R and current I. Consider a screw driver (approximated as a cylinder with radius a such that a << R ) of permeability Î¼ partially inside the solenoid and partially outside at one end. The axis of the cylinder is parallel to that of the solenoid. What is the approximate force/area exerted on the screw driver? Is the latter pulled in or expelled? 1...
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