# Magnetic flux

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.

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