A compass needle placed at a distance r from a short magnet...

A compass needle placed at a distance $r$ from a short magnet in tan $A$ position shows a deflection of $60^{\circ} .$ If the distance is increased to $r(2)^{1 / 3}$, the deflection of compass needle is
(a) $30^{\circ}$
(b) $60^{\circ}$
(c) $45^{\circ}$
(d) $0^{\circ}$

Key Concepts

Magnetic Dipole

A magnetic dipole is an idealized model of a magnet or a current loop that produces a magnetic field with both north and south poles. It is fundamental in understanding how magnets interact with their surroundings. In theoretical and practical contexts, the magnetic field of a dipole diminishes with distance, which is crucial for analyzing how the strength of the field (and therefore its effect on a compass needle) changes as you move away from the dipole.

Inverse Cube Law

The inverse cube law describes how the magnetic field of a short magnet, or a dipole, decreases with the cube of the distance from its center. This means that if the distance is increased by a certain factor, the magnetic field strength is reduced by the cube of that factor. This concept is essential when calculating changes in compass deflection as the distance from the magnet is altered.

Tangent Law in Magnetism

The tangent law in magnetism provides a relationship between the deflection angle of a compass needle and the ratio of two perpendicular magnetic field components, such as the magnet's field and the earth’s field. Specifically, the law is expressed as tan(?) = (magnet's field) / (earth's field), which is key to determining how much the needle will be deflected under the influence of multiple magnetic fields.

Superposition Principle

The superposition principle in magnetism states that the net magnetic field at any point is the vector sum of the individual magnetic fields produced by each source. This principle is used to analyze how the magnetic field from a short magnet combines with the earth’s magnetic field, resulting in a specific deflection angle of a compass needle.

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