Q.The value of magnetic induction at a distance r from a single pole is inversely proportional to

Currently Gauss's law for magnetism states the net magnetic flux through any closed surface is zero (no monopoles); if monopoles existed, the right side would instead equal mu0 times the enclosed pole strength, just like the electric case.

Gauss's law for magnetism in its present form is: the closed surface integral (over any closed surface S) of B . dA = 0, reflecting the experimental fact that isolated magnetic poles (monopoles) have never been observed - magnetic field lines always form closed loops with no starting/ending point (no magnetic 'charge'). If magnetic monopoles did exist, with an isolated pole strength qm enclosed by the surface, this law would take a form exactly analogous to Gauss's law for electric charge: …

An isolated magnetic pole of strength m produces B = (mu0/4pi)(m/r^2), an inverse-square law, so the magnetic induction is inversely proportional to r^2.

The magnetic field (magnetic induction) at a distance r from a single magnetic pole of pole strength m is given by Coulomb's law of magnetism:

B = (mu0 / 4*pi) * (m / r^2)

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Isolated magnetic monopoles (single north or south poles) do not exist in nature; magnetic poles always occur in pairs, so the magnetic dipole is the basic unit of magnetism.

Unlike electric charge, where an isolated positive or negative charge can exist, no isolated magnetic 'monopole' has ever been observed. If a bar magnet is cut into pieces, each piece becomes a smaller magnet with its own north and south pole — the poles can never be separated. This means the fundamental, indivisible unit of magne …

This statement is False — the strength (pole strength) of a bar magnet is maximum at its two ends (poles), not at its centre.

A bar magnet's magnetism is concentrated near its two ends, called the north and south poles, where the pole strength $m$ is maximum. At the exact centre of the magnet, the effects of the two equal and opposite poles (north and south) tend to cancel, so the net magnetic effect (and hence the 'strength' measurable there) is mini …

Magnetic scalar potential of a pole falls as 1/r: V = (μ₀/4π)(m/r).

By analogy with electrostatics, a magnetic pole of strength m produces a field that falls off as $1/r^2$:

$B = \frac{\mu_0}{4\pi}\frac{m}{r^2},$

and a magnetic scalar potential that falls off as $1/r$:

$V = \frac{\mu_0}{4\pi}\frac{m}{r}.$

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SI unit of magnetic pole strength = ampere-metre (A·m).

The magnetic dipole moment of a bar magnet is m = (pole strength) × (magnetic length), i.e. M = q_m × 2l. The SI unit of magnetic moment is A·m² (same as current × area). Since the magnetic length has unit metre:

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Magnetic pole strength has SI unit ampere·metre (A·m).

Magnetic pole strength m is related to magnetic moment by M = m × 2l, where 2l is the magnetic length. Since magnetic moment has unit ampere·metre² (A·m²) and length has unit metre, pole strength has unit:

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Gauss's Law for magnetism states the net magnetic flux through any closed surface is always zero — the direct proof that isolated magnetic monopoles do not exist.

Gauss's law for magnetism is written as:

$\oint \vec{B} \cdot d\vec{A} = 0$

for any closed surface. This is in contrast to Gauss's law for electric fields, $\oint \vec{E} \cdot d\vec{A} = q_{enc}/\varepsilon_0$, which is non-zero whenever a net electric charge (monopole) is enclosed.

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