Force between two identical short bar magnets whose centres...

Force between two identical short bar magnets whose centres are $r$ metre apart is $8.1 \mathrm{~N}$, when their axes are along the same line. If separation is increased to $3 r$ and the axis are rearranged perpendicularly, the force between them would become (a) $2.4 \mathrm{~N}$ (b) $1.2 \mathrm{~N}$ (c) $0.1 \mathrm{~N}$ (d) $1.15 \mathrm{~N}$

Force between two identical short bar magnets whose centres are $r$ metre apart is $8.1 \mathrm{~N}$, when their axes are along the same line. If separation is increased to $3 r$ and the axis are rearranged perpendicularly, the force between them would become
(a) $2.4 \mathrm{~N}$
(b) $1.2 \mathrm{~N}$
(c) $0.1 \mathrm{~N}$
(d) $1.15 \mathrm{~N}$

Key Concepts

Magnetic Dipole Model

Bar magnets can be approximated as magnetic dipoles when their dimensions are small compared to the separation between them. In this model, each magnet is characterized by a magnetic moment, and the interaction energy between two such dipoles can be calculated using a formula that depends on their moments, the separation distance, and their relative orientation. This abstraction is widely used in electromagnetism to study the behavior of magnets in various configurations.

Distance Dependence in Dipole?Dipole Interactions

The force between two magnetic dipoles is highly sensitive to the distance separating them, typically following an inverse power law such as 1/r^4 for the axial configuration. This means that even a modest increase in separation can dramatically reduce the force between the dipoles. Understanding this scaling law is crucial for correctly predicting how changes in distance affect the magnitude of the interaction.

Effect of Orientation on Magnetic Forces

The relative orientation of the dipoles plays a critical role in the strength and nature of the force between them. For example, when the magnetic moments are aligned along the line joining the centers (axial configuration), the interaction force is different than when the moments are arranged perpendicularly (equatorial configuration). The angular dependence in the dipole–dipole interaction formula leads to variations in the effective coefficient that multiplies the distance-dependent term, significantly influencing the force’s magnitude.

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