What is magnetic susceptibility?

Magnetic susceptibility is the measure of the extent to which a material will be magnetized in an applied magnetic field. It is denoted by χ . It is the ratio of magnetization and magnetizing field intensity. χ = M H , where M is the value of magnetization and H is the field intensity.

E M B I B E

Physics Standard 12 Vol I>Chapter -1 - Magnetism and Magnetic Effects of Electric Current>EVALUATION>Q 3

EASY

12th Tamil Nadu Board

IMPORTANT

Earn 100

Define magnetic dipole moment of a bar magnet.

Important Points to Remember in Chapter -1 - Magnetism and Magnetic Effects of Electric Current from Tamil Nadu Board Physics Standard 12 Vol I Solutions

1. The bar magnet:

(i) It has been known since ancient times that magnet tend to point in the north-south direction.

(ii) There are two poles; north pole and south pole. Like magnetic poles repel and unlike ones attract.

(iii) Magnetic monopoles do not exist. If you slice a magnet in half, you get two smaller magnets.

2. Bar magnetic in external field:

(i) When a bar magnet of dipole moment $m$ is placed in a uniform magnetic field $B$ , the force on it is zero.

(ii) The torque on it is $m \times B$

(iii) its potential energy is $- m \cdot B$ , where we choose the zero of energy at the orientation when $m$ is perpendicular to $B$ .

3. Field due to a small bar magnet:

Consider a bar magnet of size $l$ and magnetic moment $m$ , at a distance $r$ from its mid-point, where $r ≫ l$ , the magnetic field $B$ due to this bar is, $B = \frac{μ_{0} m}{2 π r^{3}}$ (along axis) and $B = - \frac{μ_{0} m}{4 π r^{3}}$ (along equator)

4. Gauss' law for magnetism:

Gauss’s law for magnetism states that the net magnetic flux through any closed surface is zero.

5. Earth's magnetism:

(i) 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.

(ii) Three quantities are needed to specify the magnetic field of the earth on its surface– the horizontal component, the magnetic declination, and the magnetic dip. These are known as the elements of the earth’s magnetic field.

(iii) A vertical plane passing through geographic axis is called geographic meridian.

(iv) A vertical plane passing through magnetic axis is called magnetic meridian.

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

6. Magnetization and Magnetic Intensity:

(i) Consider a material placed in an external magnetic field $B_{0}$ . The magnetic intensity is defined as, $H = \frac{B_{0}}{μ_{0}}$

(ii) The magnetisation $M$ of the material is its dipole moment per unit volume.

(iii) The magnetic field $B$ in the material is, $B = μ_{0} (H + M)$

(iv) For a linear material, $M = χ H$ . So that $B = μ H$ and $χ$ is called the magnetic susceptibility of the material.

(v) The three quantities $χ$ , the relative magnetic permeability $μ_{r}$ and the magnetic permeability $μ$ are related as follows: $μ = μ_{0} μ_{r}$ and $μ_{r} = 1 + χ$

7. Magnetic Properties of Materials:

(i) 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 $χ$ .

(ii) Diamagnetic substances are those which have tendency to move from stronger to the weaker part of the external magnetic field.

(iii) Paramagnetic substances are those which have tendency to move from a region of weak magnetic field to strong magnetic field.

(iv) Ferromagnetic substances are those 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.

8. Curie temperature:

(i) The temperature of transition from ferromagnetic to paramagnetism is called the Curie temperature.

(ii) Substances which at room temperature retain their ferromagnetic property for a long period of time are called permanent magnets.

9. Hysteresis:

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

10. Lorentz force:

(i) The force acting on a moving charge in a magnetic field is called as Lorenz force, and it is given by, $F = q [v \times B]$ where $q$ is the charge, $v$ is the velocity of the charge and $B$ is the magnetic field. This force is always perpendicular to the velocity of the charge, so the work done by this force on the charge is zero.

(ii) A current carrying element contains moving charges, so there will be Lorenz force on it which is given as, $F = I l \times B$ , where $I$ is the current, $l$ is its length and $B$ is the magnetic field.

(iii) A charge moving in a plane perpendicular to the magnetic field will perform circular motion with a radius of $r = m v / q B$ , where $m$ is the mass of the particle, $v$ is speed, $q$ is the charge and $B$ is the magnetic field. The angular frequency of rotation is given by $ω = 2 π ν = q B / m$ where $ν$ is the frequency.

(iv) Along with the perpendicular component, when the charge has a component of velocity parallel to the magnetic field, it will perform helical motion with a pitch given by, $p = v_{p} T = 2 π m v_{p} / q B$ , where $v_{p}$ is the component of velocity parallel to the field and $T$ is the time period of rotation.2.

11. Biot-savart law:

(i) The magnetic field produced by a current carrying element is given by the Biot-Savart law according to which, $d B = \frac{μ_{0}}{4 π} \frac{I d l \times r}{r^{3}}$ , where I is the current in the element.

(ii) The magnetic field produced by a current carrying loop along its axis is given by, $B = \frac{μ_{0} I R^{2}}{2 {(x^{2} + R^{2})}^{3 / 2}}$ where $I$ is the current in it, $R$ is the radius of it and $x$ is the distance of the point from the centre of the loop along its axis. At the centre of the loop, the field becomes, $B = \frac{μ_{0} I}{2 R}$ .

12. Ampere's circuital law:

(i) According to Ampere’s circuital law, the line integral of the field in an imaginary closed loop is given by, $∮ B \cdot d l = μ_{0} I$ , where $I$ is the current flowing through the loop.

(ii) From Ampere’s circuital law, the field around a current carrying element is given by the equation, $B = μ_{0} I / (2 π r)$ where $I$ is the current in the wire and $r$ is the perpendicular distance of the point from the wire.

(iii) Field in a Solenoid is given by the equation, $B = μ_{0} n I$ , where $n$ is the number of turns per unit length and $I$ is the current in the solenoid.

(iv) Field in a Toroid is given by the equation, $B = \frac{μ_{0} N I}{2 π r}$ , where $N$ is the total number of loops, $I$ is the current in the toroid and $r$ is its radius.

13. Force between the parallel wires:

When two parallel wires are brought close to each other, they both start attracting each other if they carry in the same direction or repel each other if the current is in the opposite direction. The equation for the force between them per unit length is given by, $F = \frac{μ_{0} I_{1} I_{2}}{2 π d}$ where $I_{1}$ and $I_{2}$ are the currents in them and $d$ is the distance between them.

14. Current loop as magnetic dipole:

(i) The dipole moment of a current carrying loop is given by, $m = N I A$ , where $N$ is the number of turns in the loop, $I$ is the current in it and $A$ is the area of the loop.

(ii) The torque acting on a current carrying loop placed in a uniform magnetic field is given by the equation, $τ = m \times B$ , where $m$ is the dipole moment of the loop and $B$ is the magnetic field. It can also be written as, $τ = I A B s i n θ$ , where $A$ is the area of the loop and $θ$ is the angle between the area and the field.

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