Figure shows a long straight wire carrying current I and a square conducting wire loop of side l, at a distance 'a' from current wire. Both the current wire and loop are in the plane of paper. Find the flux of magnetic filed of current wire, passing through the loop.

Explanation

As the field of current wire passing through the loop is same in direction (normally inward) but not uniform in magnitude.
So, we will use integtation method for finding the flux.
The same flux through a thin reactangular strip of length l and with dx, is given by
`dphi_(B)=B_(x).dS=B_((x))dScos180^(@)`.
Magnetic field due to a long straight wire carrying current I is given by `B=(mu_(0)I)/(2pix)`, and area, `dS=lxxdx`.
`therefore" "phi_(B)=intdphi_(B)=-int(mu_(0))/(2pi)(Il)/(x).dx=-(mu_(0))/(2pi)Il[log_(e)x]_(x=a)^(x=a+l)`
`=-(mu_(0))/(2pi).Illog_(e).(a+I)/(a)`