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# anothersamplefinal - Physics 604 Exam#3 Fall 10 Dr Drake...

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Physics 604 Exam #3 Fall ‘10 Dr. Drake 1. (30 points) A spherical object of radius a is immersed in a zero temperature heat bath. The sphere is heated with a δ -function source at r = r 0 . The steady state diﬀusion equation for the temperature of the sphere is - κ 2 T = ( r - r 0 ) , where 2 = 1 r 2 ∂r r 2 ∂r Solve for the radial dependence of the temperature once the temperature of the sphere has reached a steady state. Sketch the temperature versus radius. 2. (30 points) Consider a conducting, two-dimensional rectangular cavity of width a in the x direction with a bottom at y = 0 and inﬁnite extent in the positive y direction. The electric potential V is maintained at zero on the two sides and V 0 on the bottom. The potential V ( x,y ) satisﬁes Poisson’s equation 2 V = 2 ∂x 2 V + 2 ∂y 2 V = 0 (a) Write the solution for V in terms of a separable set of eigenfunctions X m ( x ) and Y m ( y ) as follows: V ( x,y ) = X m c m X m ( x ) Y m ( y ) Write equations for

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anothersamplefinal - Physics 604 Exam#3 Fall 10 Dr Drake...

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