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

Since the filed of current wire passing through the loop, is same in direction (normally inward) but not uniform in magnitude. Hence we will use integration method for finding the flux.
The small flux through a thin rectangular strip of length l and width dx, is given by
`d phi_(B)=vecB_((x)).vec(dA)=B_((x))dA cos 180^(@)=-(mu_(0))/(2pi),(l)/(x)l xx dx`
`therefore" "phi_(B)=intd phi_(B)=-int(mu_(0))/(2pi).(ll)/(x)dx=-(mu_(0))/(2pi),l.l[log_(e)x]_(x=a)^(x=a+l)`
`=-(mu_(0))/(2pi)l l log_(e)(a+l)/(a)`