Statement I: The magnetic field of a circular loop at very far away p...
Step 1: Find the magnetic field due to the circular coil on the axial line at a far away 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.
Statement I: The magnetic field of a circular loop at very far away p...
Statement 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.
Explanation:
To understand this statement, we need to understand the concept of a magnetic dipole and the magnetic field produced by a circular loop.
A magnetic dipole is a system that consists of two equal and opposite magnetic poles separated by a small distance. In the case of a circular loop, the current flowing through the loop creates a magnetic dipole. The direction of the magnetic dipole moment is perpendicular to the plane of the loop, and it depends on the direction of the current flowing through the loop.
The magnetic field produced by a magnetic dipole at a point on its axial line (the line passing through the center of the dipole and perpendicular to its plane) is given by the formula:
B = (μ₀/4π) * (2M/d³)
Where,
B is the magnetic field at the point on the axial line,
μ₀ is the permeability of free space,
M is the magnetic dipole moment of the loop (product of current and area of the loop),
d is the distance from the center of the loop to the point on the axial line.
Statement II: The magnetic field due to a magnetic dipole varies inversely with the square of the distance from the center on the axial line.
Explanation:
The formula mentioned above for the magnetic field on the axial line already demonstrates that the magnetic field due to a magnetic dipole varies inversely with the cube of the distance from the center of the dipole to the point on the axial line. Therefore, statement II is incorrect.
Conclusion:
Based on the explanations provided above, we can conclude that statement I is correct, as 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. However, statement II is incorrect, as the magnetic field due to a magnetic dipole varies inversely with the cube of the distance from the center on the axial line, not the square of the distance. Therefore, the correct option is 'A' where statement I is correct and statement II is incorrect.
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