Force between two identical bar magnets whose centers are I...

Force between two identical bar magnets whose centers are I meter apart is $4.8 \mathrm{~N}$, when their axes are in the same line. If separation is increased to $2 r$, the force between them is reduced to (a) $2.4 \mathrm{~N}$ (b) $1.2 \mathrm{~N}$ (c) $0.6 \mathrm{~N}$ (d) $0.3 \mathrm{~N}$

Force between two identical bar magnets whose centers are I meter apart is $4.8 \mathrm{~N}$, when their axes are in the same line. If separation is increased to $2 r$, the force between them is reduced to
(a) $2.4 \mathrm{~N}$
(b) $1.2 \mathrm{~N}$
(c) $0.6 \mathrm{~N}$
(d) $0.3 \mathrm{~N}$

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Key Concepts

Magnetic Dipole-Dipole Interaction

This concept refers to the interaction between two magnetic dipoles, where each magnet can be approximated by a dipole moment. The force between these dipoles depends on both the magnitude of their magnetic moments and their relative orientation and distance. In many practical cases, especially when the magnets are aligned along the same axis, the interaction can be treated using dipole-dipole formulas, which predict how the magnetic forces vary with separation.

Inverse Power Law Dependence

Many forces in physics, including the force between magnetic dipoles in certain configurations, obey an inverse power law, meaning that the force decreases as a power of the distance between the objects. For example, in an ideal dipole-dipole interaction along the axis, the force often scales as the inverse fourth power of the separation distance. This makes it possible to predict how the force changes when the distance is altered, such as determining that doubling the distance drops the force by a specific factor.

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