Magnetic Field Flux Through a Circular Loop Near an Infinite Wire

[Mandeep Deka]

1. A circular loop, (of radius 'a') is placed with its center at a distance 'r' from an infinitely long current carrying wire, (carrying current 'I'), in the same plane as that of the wire. For, a<r, find the flux of magnetic field through the loop.



2. Differential Flux=B.dA, whose integral over a surface gives the net flux through the surface. B (at a distance x, for a infinitely straight wire carrying current I)= (mu naught. i)/2.pi.x.



3. Since the magnetic field,(B) due to a infinite st. wire is a function of perpendicular distance (x) from the wire, we consider an elementary rectangular segment of plane , enclosed by the loop at a distance (r+x) from the wire with length l=2[(a^2-x^2)^0.5] and breadth dx (differential increment in perpendicular distance from the wire). So now if we have the elementary flux as (B.l.dx), we can integrate x, in the expression from -a to +a, to obtain the flux. But the integration is a bit complicated, (though the answer be determined) which puts me into a little doubt whether my approach to solve the problem is correct! I would like u to solve the problem and check whether my process is correct or not.

 

[kuruman]

Your method is correct and, yes, it leads to a complicated integral. If it makes you feel any better, this problem (in my opinion) does not teach you any new physics beyond what the simpler case of the rectangular loop parallel to the wire teaches.

 

[Mandeep Deka]

ya m aware of that.. i jus wanted to know if i was havng the corrrct approach...
by d way thanks.