A long cylindrical conductor of cross-sectional area A and radius a is made of material whose resistivity depends only on a distance r from the axis of conductor, given by `rho = c/r^(2)`, where c is a constant. Find the resistance per unit length of the conductor and the electric field strength due to which a current I flows in it.
Text Solution
AI Generated Solution
To find the resistance per unit length of a long cylindrical conductor with a varying resistivity, we will follow these steps:
### Step 1: Understanding the Geometry and Resistivity
We have a long cylindrical conductor with a radius \( a \) and a cross-sectional area \( A \). The resistivity \( \rho \) of the material is given by:
\[
\rho = \frac{c}{r^2}
\]
where \( c \) is a constant and \( r \) is the distance from the axis of the cylinder.
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