What is a magnetic axis ?

1. Magnets :

The property by virtue of which a substance can attract iron fillings (magnetic materials) is called magnetism. A body having the property of magnetism is known as a magnet. Types of magnets :

(i) Natural Magnets : Pieces of naturally occurring iron ore known as magnetite $\left(F{e}_3{O}_4\right)$. These have weak magnetism and irregular shapes.

(ii) Artificial or permanent Magnets: These are powerful magnets made of hard steel, alloys and prepared in labs. Each atom in these magnets behave like a magnetic dipole.

2. Properties of a magnet : 

(i) Poles of magnet : Every magnet has south and north pole.

(ii) Attractive Property : A magnet attracts small pieces of iron.

(iii) Directional Property : A freely suspended bar magnet always aligns in geographical north-south directions.

(iv) Nature of force between magnetic poles : Like poles of magnet repel while unlike poles attract.

(v) Poles always exist in pairs : Magnetic monopoles do not exist.

3. Bar magnet:

(i) Magnet in shape of rod or bar.

(ii) The distance between two ends of magnet is its geometric length, the distance between south and north pole of magnet is its magnetic length. Magnetic length is $84\%$ its geometric length.

(iii) Magnetic moment of bar magnet is a vector quantity equal to the product of its pole strength and magnetic length and its SI unit is Weber-metre.

4. Magnetic dipole : 

A combination of two opposite magnetic poles of equal strength separated by a small distance.

5. Magnetic field : 

Magnetic field of a magnet is the modified region of space surrounding it, in which another magnetic pole brought in experiences a force.

6. Magnetic lines of force : 

A magnetic line of force is defined as a line, straight or curved, such that the tangent to it at any point gives the direction of magnetic field at that point.

7. Properties of magnetic lines of force:

(i) These leave from N-pole and enter at S-pole and are hence, continuous curve.

(ii) Two lines of forces do not intersect.

(iii) Density of lines is greater in region of strong electric field and lesser in region of weak electric field. 

8.  Coulomb's law of magnetism :

Let $m_1$ and $m_2$ be pole strength of two magnetic poles separated by a distance $r$, by coulomb's law, force of attraction between them, $F=k\frac{m_1{m}_2}{r^2}$, $k$ is the constant of proportionality.

9. Coulomb's law in different system of units :

(i) Coulomb's law in c.g.s(emu) system : $k=1$, $F=\frac{m_1{m}_2}{r^2}$

(i) Coulomb's law in S.I. system : $k=\frac{{\mu }_0}{4\mathrm{\pi }}$ where ${\mu }_0=4\mathrm{\pi }\times {10}^{-7} \mathrm{Wb}/\mathrm{A}-\mathrm{m}$ is permeability of free space, $F=\frac{{\mu }_0}{4\mathrm{\pi }}\frac{m_1{m}_2}{r^2}$

10. Magnetic Induction :

If a north pole of strength $m_0$experiences a force $\overrightarrow{F}$ at any point then the magnetic induction or magnetic flux density at that point is $\overrightarrow{B}=\frac{\overrightarrow{F}}{m_0}$. Its SI unit is Tesla and C.G.S unit is gauss.

11. Magnetic induction or magnetic field due to an isolated magnetic pole :

The magnetic field due to an isolated magnetic pole of strength $m$ at a distance $r$ from the pole, $B=\frac{{\mu }_0}{4\mathrm{\pi }}\frac{m}{r^2}\hat{r}$, $\hat{r}$ is unit vector along the length of the pole.

12. Magnetic Intensity or magnetising field :

Magnetic intensity $\left(\overrightarrow{H}\right)$  at a point in a magnetic field is the ratio of magnetic field at that point to permeability of medium, $\overrightarrow{H}=\frac{\overrightarrow{B}}{{\mu }_0}=\frac{1}{4\mathrm{\pi }}.\frac{m}{r^2}\hat{r}$.

13. Magnetic potential :

The magnetic potential due to a pole of strength $m$ at a distance $r$ from the pole in air is given by $V=\frac{{\mu }_0}{4\mathrm{\pi }}\frac{m}{r}$.

14.  Magnetic induction or magnetic field due to a bar magnet :

(a) At a point on its axis (End-on-position)

Magnetic field at the end-on position of a bar magnet of length $2l$ and pole strength $m$ at a distance $d$ from the centre of the magnet is $B=\frac{{\mu }_0}{4\mathrm{\pi }}\frac{2Md}{{\left(d^2-l^2\right)}^2}$, where $M=2ml$ is the magnetic moment of the magnet. For $l<<d$, $B_P=\frac{{\mu }_0}{4\mathrm{\pi }}\frac{2Md}{d^3}$

(b) At a point on its equatorial line (Broad-side-on position)

The magnetic field at broad side-on position of magnet is $B=\frac{{\mu }_0}{4\mathrm{\pi }}\frac{M}{{\left(d^2+l^2\right)}^{3/2}}\hat{r}$ and for $l<<d$, $B_Q=\frac{{\mu }_0}{4\mathrm{\pi }}\frac{M}{d^3}\hat{r}$

(c) At any point : The magnetic field at a general point due to bar magnet is $B=\frac{{\mu }_0}{4\mathrm{\pi }}\frac{M}{d^3}\sqrt{1+3{\cos }^2\left(\theta \right)}$

15.  Torque experienced by a bar magnet or a magnetic dipole in a uniform magnetic field : 

Torque on a magnetic dipole of magnetic  dipole moment $\overrightarrow{M}$ in a magnetic field $\overrightarrow{B}$ is $\overrightarrow{T}=\overrightarrow{M}\times \overrightarrow{B}$

16. Work done in rotating a bar magnet in a uniform magnetic field :  

Work done by external agent to move bar magnet from ${\theta }_1$ to ${\theta }_2$ w.r.t magnetic field $\left(B\right)$ is $W=MB\left(\cos \left({\theta }_1\right)-\cos \left({\theta }_2\right)\right)$

Potential energy of a magnet in a uniform magnetic field: $U=-MB$

17. Terrestrial magnetism:

Terrestrial magnetism or the earth’s magnetic field resembles that of a (hypothetical) magnetic dipole located at the centre of the earth. The pole near the geographic north pole of the earth is called the north magnetic pole. Similarly, the pole near the geographic south pole is called the south magnetic pole.

18. Some terms connected with geomagnetism :

(i) Geomagnetic axis : It is the axis of geomagnet, which cuts earth's surface at magnetic north and south pole.

(ii) Geographical axis : The axis about which earth rotates.

(iii) Magnetic axis : Line joining north and south pole of a freely suspended magnet.

(iv) Magnetic equator : Plane perpendicular to magnetic axis of earth and which intersects all points where a magnetic needle aligns parallel to earth's surface.

(v) Magnetic meridian : A vertical plane passing through magnetic axis of freely suspended magnet.

(vi) Geographic meridian : A vertical plane passing through geographic axis.

19. Magnetic elements of earth :

a) Declination: The angle between magnetic meridian at a point with the geographical meridian is called the declination or magnetic declination.

b) Inclination or dip $\left(\delta \right)$: The angle between Earth's magnetic field with the horizontal direction in magnetic meridian at a place.

c) Horizontal component of earth's magnetic field $\left(B_H\right)$: Horizontal component of earth’s magnetic field is component of earth’s magnetic field in horizontal direction.

20. Apparent dip :

It is the angle of dip in a vertical plane other than magnetic meridian.

21. Neutral Point : 

Neutral point is a point in the region around a magnet where its magnetic field is neutralized by the horizontal component of earth's magnetic field.

(a) North Pole pointing towards north : The magnetic field of the bar magnet at these neutral points ,$B=B_{H }=\frac{{\mu }_0}{4\mathrm{\pi }}.\frac{M}{{\left(d^2+l^2\right)}^{3/2}}$

(b) North pole pointing towards south: The magnetic field of the bar magnet at these neutral points , $B=B_{H }=\frac{{\mu }_0}{4\mathrm{\pi }}.\frac{2Md}{{\left(d^2-l^2\right)}^{3/2}}$

(ii) Neutral point due to single pole: Only one neutral point is obtained in this case. 

(a) When north pole is on horizontal plane, $B=B_{H }=\frac{{\mu }_0}{4\mathrm{\pi }}.\frac{M}{d^2}$

(b) When south pole is on horizontal plane,$B=B_{H }=\frac{{\mu }_0}{4\mathrm{\pi }}.\frac{M}{d^2}$

22. Magnetic properties of materials : 

The degree of alignment of magnetic moments of atoms increases with increase in strength of magnetic field and with decrease of temperature.

23. Intensity of magnetization (I) : 

It is defined as the pole strength per unit area, area being perpendicular to the direction of magnetisation.

24. Magnetic Intensity or Magnetizing field:

Consider a material placed in an external magnetic field B0. The magnetic intensity is defined as, H=B0μ0

The magnetisation M of the material is its dipole moment per unit volume.

25. Magnetic induction or magnetic flux density $B$:

The magnetic field in the material is, $B={\mu }_0(H+1)$

26. Magnetic susceptibility $\left(\chi \right)$:

For a linear material, M=χH. So that B=μH and χ is called the magnetic susceptibility of the material.

27. Permeability :

It is defined as the ratio of magnetic induction in material to the magnetising field, $\mu =\frac{B}{H}$

The three quantities χ, the relative magnetic permeability ${\mu }_{\mathit{r}}$ and the magnetic permeability μ are related as follows: μ=μ0μr and μr=1+χ

28. Curie's Law:

The susceptibility of an unsaturated paramagnetic substance is inversely proportional to its absolute temperature. $\chi =\frac{C}{T}$, where $C$ is the curie's constant.

29.  Classification of  magnetic materials:

 Magnetic materials are broadly classified as: diamagnetic, paramagnetic, and ferromagnetic. For diamagnetic materials χ is negative and small and for paramagnetic materials it is positive and small. Ferromagnetic materials have large χ.

30.  Diamagnetic substances:

Substances which have tendency to move from stronger to the weaker part of the external magnetic field.For diamagnetic material, $\chi <0, B<{\mu }_{0}H, {\mu }_r<1$.

It is a universal phenomenon.

31. Paramagnetic substances:

Substances which have tendency to move from a region of weak magnetic field to strong magnetic field.

For paramagnetic material,$\chi >0, B>{\mu }_{0}H, {\mu }_r=\chi +1$

32. Ferromagnetic substances:

Substances which gets strongly magnetised when placed in an external magnetic field. They have strong tendency to move from a region of weak magnetic field to strong magnetic field.

For Ferromagnetic material, $B>>{\mu }_{0}H, {\mu }_r=\chi +1$

33. Hysteresis:

For a given value of $H, B$ is not unique but depends on previous history of the sample. This phenomenon is called hysteresis.

34. Soft Iron and Steel :

Soft Iron: It is a ferromagnetic material which can easily be magnetised and demagnetised. Its retentivity and coercive forces are small. It's used for making electromagnets.

Steel : It is a hard ferromagnetic material. It can easily be magnetised but cannot be magnetised by stray fields. It is used for making permanent magnets.

35. Tangent Law :

The law states that if a freely suspended magnet is subjected to two uniform magnetic fields $B$ and $B_e$ at right angles to each other, if the magnet makes an angle $\theta$ with latter field, $B=B_e\tan \left(\theta \right)$.

(i) Restoring couple : The torque of restoring couple formed by applying magnetic field on two poles of magnet each having equal and opposite strength, ${\tau }_1=mB.2l.\sin \left(\theta \right)$

(ii) Deflecting couple :The torque of deflecting couple is ${\tau }_2=mB.2l.\cos \left(\theta \right)$

Principle of tangent galvanometer is based on tangent law.