Mathematics

Problem

Current density in a cylindrical wire of radius

R

is given as

J=\begin{cases} J_0\left(\frac{x}{R}-1\right) & \text{for } 0\leq x<\frac{R}{2}\\ J_0\frac{x}{R} & \text{for } \frac{R}{2}\leq x\leq R \end{cases}

If the current flowing in the wire is

\frac{k}{12}\pi J_0 R^2

, find the value of

k