Problem Set 5

# Problem Set 5 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Spring 2008 Problem Set 5 Due: Wednesday, March 12 at 11 am. Hand in your problem set in your section slot in the boxes outside the door of 32- 082. Make sure you clearly write your name, section, table, group (e.g. L01 Table 3 Group A) Problem 1: Non-uniform Conductivity (10 points) A cylindrical glass rod is heated with a torch until it conducts enough current to cause a light bulb to glow. The rod has a length L = 2 cm, a diameter d = 0.5 cm, and its ends, plated with material of infinite conductivity, are connected to the rest of the circuit. When red hot, the rod’s conductivity varies with position x measured from the center of the rod as 44 0 (x) L x σσ = , with σ 0 = 4 × 10 2 ( Ω− m ) 1 . a) What is the resistance of the glass rod? Express your answer both symbolically and as a value in ohms. b) When a voltage Δ V is applied between the two ends, what is the current density () x J G and what is the steady-state electric field x E G ?

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Problem Set 5 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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