I: The magnetic field of a circular loop at very far away point on t...
Step 1: Find the magnetic field due to the circular coil on the axial line at a far away distance.
This is same as the magnetic field due to bar magnetic on axial line at a far distance.
Step 2: Find the magnetic field due to bar magnet on the axial line.
The magnetic field due to magnetic dipole varies inversely with the cube of the distance from the center on the axial line.
I: The magnetic field of a circular loop at very far away point on t...
Explanation:
I. The magnetic field of a circular loop at a very far away point on the axial line varies with distance as like that of a magnetic dipole.
The magnetic field of a circular loop at a very far away point on the axial line can be approximated as that of a magnetic dipole. When we consider a circular loop carrying a current, it generates a magnetic field around it. This magnetic field can be represented as a magnetic dipole with the axis passing through the center of the loop.
II. The magnetic field due to a magnetic dipole varies inversely with the square of the distance from the center on the axial line.
The magnetic field due to a magnetic dipole follows an inverse square law. This means that as the distance from the center of the dipole increases, the magnetic field decreases rapidly. Mathematically, the magnetic field (B) at a point on the axial line of the dipole is given by:
B = μ₀m/(4πr²)
where B is the magnetic field, μ₀ is the permeability of free space, m is the magnetic moment of the dipole, and r is the distance from the center of the dipole.
From the given information, we can conclude that both statements are correct.
- Statement I states that the magnetic field of a circular loop at a very far away point on the axial line varies as that of a magnetic dipole, which is true.
- Statement II states that the magnetic field due to a magnetic dipole varies inversely with the square of the distance from the center on the axial line, which is also true.
Therefore, the correct answer is option 'A': I is correct and II is incorrect.
In summary, the magnetic field of a circular loop at a very far away point on the axial line can be approximated as that of a magnetic dipole, and the magnetic field due to a magnetic dipole varies inversely with the square of the distance from the center on the axial line.
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