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Explain the magnetic susceptibility (chi) of material. From it explain relative magnetic permeability of material and magnetic permeability of material. Obtain the relation between them. |
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Answer» Solution :The MAGNETISATION of material M proportional to the magnetic intensity (H). `overset(to) (M) prop overset(to) (H)` `therefore overset(to) (M) = chi overset(to) (H) ""…(1)` Here `chi` is dimensionless QUANTITY called it as the magnetic susceptibility. It is a measure of how a magnetic material responds to an external field. For paramagnetic material it is small and positive. For DIAMAGNETIC material it is small and negative because this material `overset(to) (M) and overset(to)(H)` are opposite in direction. Think the material which can be magnetize are filled in interior of solenoid. Total magnetic field obtain when current I in solenoid pass through is, `overset(to) (B) = mu_(0) (overset(to) (H) + overset(to) (M) )""...(2)` From equation (1) and (2), `overset(to) (B) = mu_(0) (overset(to) (H) + chi overset(to) (H) )` `therefore overset(to) (B) = mu_(0) (1+ chi) overset(to) (H)""...(3)` Here `mu_(0) (1 + chi) ` is the permeability `mu` of the material. Hence, `mu= mu_(0) (1 + chi) ""...(4)` `(mu) /( mu_0) = (1 + chi ) = mu_r""...(5)` `therefore mu= mu_(0) (1 + chi) = mu_(0) mu_r ""...(6)` Here, (1) `mu_r` is called the relative magnetic permeability of the substance. It is a dimensionless quantity. It is the analog of the dielectric constant in electrostatics. (2) Equation (6) indicates the interrelation between `mu, mu_r and H` and only ONE of them is independent. Given one the other two MAY be easily determined. Putting equation (6) in equation (3), `overset(to) (B) = mu_(0) mu_r overset(to) (H)""...(7)` `overset(to) (B) = muoverset(to) (H) ( because mu_(0) mu_(r) = H) ""...(8)` |
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