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The mass of a specimen of a ferromagnetic material is $0.6kg$ and its density is $7.8 \times {10^3}kg/{m^3}$. If the area of hysteresis loop of alternating magnetising field of frequency $50Hz$ is $0.722MKS$ units then the hysteresis loss per second will be:
A) $277.7 \times {10^{ - 5}}joule$
B) $277.7 \times {10^{ - 6}}joule$
C) $277.7 \times {10^{ - 4}}joule$
D) $27.77 \times {10^{ - 4}}joule$

Last updated date: 17th Apr 2024
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Hint:Whenever a magnetic field is present in a material or a system, then hysteresis occurs. When a ferromagnetic material is magnetized, the magnetization intensity denoted by ‘B’ lags behind the magnetic field intensity denoted by ‘H’. This process is known as hysteresis.

Complete step by step solution:
The energy that is wasted due to hysteresis in the form of heat is known as hysteresis loss. All the ferro magnetic substances undergo hysteresis. The hysteresis loss per second in the material is given by the formula
$ \Rightarrow E = \nu AVt$
Where E is the energy loss due to hysteresis
$\nu $ is the frequency
V is the volume which is the ratio of mass and volume
‘t’ is the time
$ \Rightarrow E = \nu A\dfrac{m}{\rho }t$
‘m’ is the mass and
$\rho $ is the density
Substituting the values given in the above equation and solving for energy loss
$ \Rightarrow E = 50 \times 0.722 \times \dfrac{{0.6}}{{7.8 \times {{10}^3}}} \times 1$
$E = 277.7 \times {10^{ - 5}}Joule$
The hysteresis loop per second for the ferromagnetic material will be
$E = 277.7 \times {10^{ - 5}}joule$

Option A is the right answer.

Note: It is important to note that if a ferromagnetic material is placed inside a magnetic field then due to the presence of a magnetic field, the molecules of the material get aligned in one direction and it gets magnetised. On the other hand, if the direction of the current is reversed, then the ferromagnetic material will get demagnetised. So the relationship between the magnetizing field and the intensity of magnetisation is given by using a hysteresis loop. The hysteresis loop shows the area required to complete one cycle of magnetisation and demagnetisation.