Solution Found!
Suppose the conductivity of the material separating the
Chapter 7, Problem 4P(choose chapter or problem)
Problem 4P
Suppose the conductivity of the material separating the cylinders in Ex. 7.2 is not uniform; specifically, σ(s) = k/s, for some constant k. Find the resistance between the cylinders. [Hint: Because σ is a function of position, Eq. 7.5 does not hold, the charge density is not zero in the resistive medium, and E does not go like 1/s. But we do know that for steady currents I is the same across each cylindrical surface. Take it from there.]
Questions & Answers
QUESTION:
Problem 4P
Suppose the conductivity of the material separating the cylinders in Ex. 7.2 is not uniform; specifically, σ(s) = k/s, for some constant k. Find the resistance between the cylinders. [Hint: Because σ is a function of position, Eq. 7.5 does not hold, the charge density is not zero in the resistive medium, and E does not go like 1/s. But we do know that for steady currents I is the same across each cylindrical surface. Take it from there.]
ANSWER:
Step 1 of 2
We have to find the resistance between the cylinders if the conductivity of the material separating the cylinders is not uniform and it is of the form for some constant
The current flowing from one cylinder to the other is given by,
But
So,
