Question

to A very long cylindrical shell of inner radius a and outer radius 2a is made of a conducting material of conductivity o= kr, where k is a constant and r is measured perpendicularly from the axis of the shell. A potential difference AV is applied across the inner and outer surfaces of the shell, with the inner surface at the higher potential. (a) What is the resistance dR per unit length of the cylinder, for a thin cylindrical shell between r and r + dr? (Note that the current flows radially outward, not along the axis of the cylinder.) (b) Integrate dR over r from r = a to r = 2a to find R, the resistance per unit length of the cylinder. (b) Given R above, what is the resulting current I per unit length? (c) What is the current density j and the electric field at r = 1.5a? MacBook Pro

Answer 1

1. (a) da selecting a thin cylindrical shell of raders r and thickness dr and length i'. Its Resistance can be written as: Ix dr - ar - 5 zar 1. kr. aar L Unit length, L= t = dR= 27 K r² - X 1 d R = Ć . dr For Answer 2a (b) Integrating: sdr = I do not a R=(ankende = waka. Anar (CI I= AV = 4kka Av Answer KK a.

(d) т . : чка ДV - чKAV дах (1-S) 3 Area Answer & E: г. е YAV су Answer ч. 5 а.