A long copper wire carries a current of `I` ampere. Calculate the magnetic flux per meter of the wire for a plane surface `S` inside the wire as shown in Fig.

Explanation

Consider an element of width `dr` at a distance `r` from the axis of the wire. The field due to the current `I` in the wire at the position of element will be `B = (mu_(0)Ir)/(2piR^(2))`.
And as its direction is perpendicular to the plane surface, flux linked with the element is given by
`dphi = B ds cos theta = (mu_(0))/(2pi)(I)/(R^(2))r (1 dr)cos theta`

So, the flux linked with the plane surface is given by
`phi = (mu_(0))/(2pi)(I)/(R^(2))int_(0)^(R) r dr = (mu_(0)I)/(4pi)`