Magnetism and Columb's Law

Magnetism is one of the phenomena by which materials exert an attractive or repulsive force on other materials. All materials are influenced by the presence of a magnet, but the degree of influence may be greater or lesser on them. Unlike other material characteristics, magnetic properties cannot be seen, heard, tasted or felt directly which makes the concept difficult to understand.

Magnetism is familiar to us in our daily life. Most of the electronic devices such as an electric doorbell, drill machine, microwave oven, and vacuum cleaner and so on have magnets. Magnetism was discovered by

Greeks and Chinese before 600 B.C. In the year 1820, Hass Oersted discovered that an electric current would deflect a magnetic needle, magnetism, and electric field are related to each other.

Some Properties of Magnet

Attractive properties: A magnet attracts small pieces of ferromagnetic materials like iron, nickel, cobalt, and their alloys. The force of attraction is greater at near distances but smaller at far distances.

A pair of poles: Every magnet has two poles north and south where most of its strength is concentrated.

Directive properties: A bar magnet suspended freely about its center of gravity by a thread aligns itself along the north-south direction.

Inducing properties: In a bar of iron placed near magnets attracts other magnetic substance, in the presence of the magnet, iron bar is magnetized and gets two poles. This phenomenon is called magnetic induction.

Force between poles: The force between two unlike poles is attractive and that between like poles are repulsive.

Coulomb’s Law

Coloumb’s law states that the force between two poles is directly proportional to the products of the strengths of the poles and inversely proportional to the square of the distance between them.

Let m₁ and m₂ be a strength of two poles separated at a distance r. The magnitude of force is given by

\begin{align*} F &\propto \frac {m_1m_2}{r^2} \\ \text {or,} \: F &= K \frac {m_1m_2}{r^2} \\ \text {where k is a proportionality constant.} \\ \text {In CGS-system.} \\ \text {K}= 1 \\ \text {and we have} \\ F = K\frac {m_1m_2}{r^2} \\ \text {In SI-units,} \: k = \frac {\mu_0}{4\pi }\: \text {and the force between the poles is} \\ F &= \frac {\mu_0}{4\pi } \frac {m_1m_2}{r^2} \\\end{align*}

\(\mu _o\) is the permeability of a free space or vacuum which has a value of \(4\pi \times 10^{-7} \: N/A^2\).when the poles of the magnets are in a medium of permeability \(\mu\), then force between them is

$$ F = \frac {\mu }{4\pi } \frac {m_1m_2}{r^2} $$

The permeability of a medium indicates by how much amount the magnetic force is transferred compared to the vacuum. It is the ability of a material to modify a magnetic field that is applied to it. The dimension of the permeability is [MLT^-2A^-2]. Using the dimensional analysis, unit of pole strength comes to Am in SI-units.

Reference

Manu Kumar Khatry, Manoj Kumar Thapa,et al.Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.