Name: Tangent Galvanometer: Theory and Construction
Uploaded: 2019-07-19
Duration: 4 min 47 s
Description: When you heard of a tangent galvanometer, what strikes your mind? Don't you think this is related to tangent? Watch this video to know the science behind it.

Question

Define terms magnetic permeability and magnetic susceptibility. Derive relation between relative permeability and susceptibility.

Accepted Answer

Magnetic susceptibility states the degree of magnetization of a material in respect to an applied magnetic field. Permeability is the property of material in which a material is tried to form a magnetic field within itself. The measure of this ability to form magnetic field is known as permeability.

Magnetic susceptibility $χ_{m}$ indicates the intensity or the degree of magnetization $(I)$ of a material in response to the intensity of the magnetizing force $(H)$ of the applied magnetic field $(B) .$ In other words, it describes the magnetizability of a material. This is a dimensionless proportionality constant. A higher susceptibility implies that the material is more susceptible to the field and hence can be easily magnetized.

Magnetic susceptibility is given as $χ_{m} = \frac{I}{H},$ Where $I$ is the intensity of magnetization and $H$ is the intensity of the magnetizing field (magnetizing force of applied field).

Magnetic permeability is a property of the material that characterises the amount of magnetizing force $(H)$ that a material experiences under the influence of an applied magnetic field $(B) .$

And it is given as: $μ = \frac{B}{H}$

Relative permeability is the ratio of the permeability of the material $(μ)$ to that of free space $(μ_{\circ}) .$

And it is given as: $μ_{r} = \frac{μ}{μ_{\circ}}$

Now, let us calculate the net field inside a magnetic material.

The net field will be a resultant of magnetization due to applied field $(B_{\circ})$ and magnetization due to induced magnetism $(B_{i}),$

$∴ B = B_{\circ} + B_{i}$

Where, $B_{\circ} = μ_{\circ} H$ and $B_{i} = μ_{\circ} I$

$∴ B = μ_{\circ} (H + I)$

$\frac{B}{H} = μ_{\circ} (1 + \frac{I}{H})$

Substituting $μ = \frac{B}{H}$ and $χ_{m} = \frac{I}{H}$ in the above equation, we get:

$μ = μ_{\circ} (1 + χ_{m})$ $\Rightarrow \frac{μ}{μ_{\circ}} = (1 + χ_{m}) \Rightarrow μ_{r} = (1 + χ_{m})$

Hence, Relative permeability in terms of susceptibility: $μ_{r} = (1 + χ_{m})$

Define terms magnetic permeability and magnetic susceptibility. Derive relation between relative permeability and susceptibility.

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