Magnetic Field Flux Through a Circular Loop Near an Infinite Wire

In summary, the conversation discusses finding the flux of magnetic field through a circular loop placed at a distance from an infinitely long current carrying wire. The formula for differential flux and the magnetic field at a distance from the wire are also mentioned. The conversation concludes by confirming that the approach used to solve the problem is correct, although the resulting integral may be complicated.
  • #1
Mandeep Deka
104
0
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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  • #2
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.
 
  • #3
ya m aware of that.. i jus wanted to know if i was havng the corrrct approach...
by d way thanks.
 

1. What is magnetic field flux?

Magnetic field flux is a measure of the amount of magnetic field passing through a given area. It is represented by the symbol Φ and is measured in units of webers (Wb).

2. How is magnetic field flux calculated?

The magnetic field flux through a surface is calculated by multiplying the magnetic field strength (B) by the area of the surface (A) and the cosine of the angle between the magnetic field and the surface. This can be represented by the equation Φ = B * A * cos(θ).

3. What is a circular loop?

A circular loop is a closed, circular-shaped wire or coil that conducts electrical current. It is often used in experiments to study the effects of magnetic fields.

4. What is an infinite wire?

An infinite wire is a theoretical concept used in physics to simplify calculations involving magnetic fields. It assumes that the wire is infinitely long and has a constant current flowing through it, resulting in a constant magnetic field surrounding the wire.

5. How does a circular loop near an infinite wire affect the magnetic field flux?

A circular loop near an infinite wire will experience a changing magnetic field as the current flows through the wire. This changing magnetic field induces an electric current in the circular loop, which in turn creates its own magnetic field. As a result, the magnetic field flux through the loop is affected and can be calculated using the equation mentioned in question 2.

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