Question

Solenoid has a core of material with relative permittivity of 500. The windings of the solenoid are insulated from the core and carry a current of 2 A. If the number of terms is 1000 per meter, then magnetization is?

A.)7.78 $\times 10^5$ $Am^{-1}$
B.)8.88 $\times 10^5$ $Am^{-1}$
C.)9.98 $\times 10^5$ $Am^{-1}$
D.)10.2 $\times 10^5$ $Am^{-1}$

Answer 1

Hint: Find out the magnetic intensity and use the definition of magnetic susceptibility of a material in terms of relative permittivity and then use the the magnetic susceptibility and the magnetic intensity to find the amount of magnetization using the relation between magnetic intensity and amount of magnetization.

Step by step solution:
we are given the number of turns per meter of the solenoid as n = 1000
the current in the solenoid is given as 2 A
we know that the definition of magnetic intensity is given by in terms of current and number of turns as H = nI
Where is the magnetic field intensity n is the number of turns and I is the amount of current in the coils.
from the given values we get the magnetic intensity as H= $1000 \times 2 ms^{-1}$

Now let us use the definition of magnetic susceptibility of the material in terms of relative permittivity. we know the relation between magnetic permeability and the magnetic susceptibility is given as $\mu_r = 1 + X$

Where $\mu_r$ is the relative permittivity and the X is the magnetic susceptibility.
we are given the value of relative permittivity as 500
So we get the value of the magnetic susceptibility X = $\mu_r -1 = 500 - 1 = 499$
having found the magnetic susceptibility and the magnetic intensity in the solenoid we can now find the magnetization as below

The relation between magnetization and magnetic intensity is given by M = XH
We get M = 499 $\times$ 2000 = $9.98\times 10^{5} A m^{-1}$. So option C is correct.

Note: One of the concepts where usually many students may confuse is the difference between the magnetic intensity and the magnetization. magnetic intensity Indicates the total amount of equivalent current flowing in the coil. Whereas magnetization depends upon the nature of the material which may indicate using the term magnetic susceptibility and the magnetic intensity or the amount of current flowing in the coil.