The magnetic field at a point x on the axis of a small bar magnet is equal to the at a point y o

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The magnetic field at a point x on the axis of a small bar...

The magnetic field at a point $\mathrm{x}$ on the axis of a small bar magnet is equal to the at a point $\mathrm{y}$ on the equator of the same magnet. The ratio of the distances of $\mathrm{x}$ and $\mathrm{y}$ from the centre of the magnet is (a) $2^{-3}$ (b) $2^{-(1 / 3)}$ (c) $2^{3}$ (d) $2^{+(1 / 3)}$

The magnetic field at a point $\mathrm{x}$ on the axis of a small bar magnet is equal to the at a point $\mathrm{y}$ on the equator of the same magnet. The ratio of the distances of $\mathrm{x}$ and $\mathrm{y}$ from the centre of the magnet is
(a) $2^{-3}$
(b) $2^{-(1 / 3)}$
(c) $2^{3}$
(d) $2^{+(1 / 3)}$

Key Concepts

Magnetic Dipole

A magnetic dipole is a simplified model used to represent a bar magnet or a current loop, characterized by a magnetic moment. This model captures the essential features of the magnetic field distribution around a magnet, allowing for the derivation of field expressions in different regions.

Axial Magnetic Field

The axial magnetic field is the component of a dipole’s magnetic field measured along the line that passes through the center of the dipole. It is described by an inverse cube law with distance, multiplied by a coefficient that reflects the contribution of the magnetic moment, and typically has a stronger magnitude compared to the equatorial field at the same distance.

Equatorial Magnetic Field

The equatorial magnetic field is the component measured in the plane perpendicular to the dipole's axis, where the magnetic field strength is lower than that along the axis. This field also decreases with distance according to an inverse cube law but includes a different multiplicative factor that makes it distinct from the axial field.

Inverse Cube Law and Field Equations

Both the axial and equatorial magnetic fields of a dipole decay with distance according to an inverse cube law. The specific coefficients in the field equations, which differ between the axial and equatorial directions, are crucial for comparing field strengths at different points and for determining relationships like the distance ratio at which the fields become equal.

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