Answer the following questions:
$(a)$ Explain qualitatively on the basis of the domain picture the irreversibility in the magnetisation curve of a ferromagnet.
$(b)$ The hysteresis loop of a soft iron piece has a much smaller area than that of a carbon steel piece. If the material is to go through repeated cycles of magnetisation,which piece will dissipate greater heat energy?
$(c)$ '$A$ system displaying a hysteresis loop such as a ferromagnet,is a device for storing memory?' Explain the meaning of this statement.
$(d)$ What kind of ferromagnetic material is used for coating magnetic tapes in a cassette player,or for building 'memory stores' in a modern computer?
$(e)$ $A$ certain region of space is to be shielded from magnetic fields. Suggest a method.

(N/A) The hysteresis curve ($B-H$ curve) of a ferromagnetic material is shown in the figure.
$(a)$ In a ferromagnet,the material is composed of small regions called domains,each having a spontaneous magnetization. When an external magnetic field $H$ is applied,these domains align themselves. The process of domain wall movement and rotation is not perfectly reversible due to pinning by impurities or crystal defects. Thus,when $H$ is removed,the domains do not return to their original random orientation,leading to residual magnetization and irreversibility.
$(b)$ The heat energy dissipated per unit volume per cycle is equal to the area of the hysteresis loop. Since the carbon steel piece has a larger hysteresis loop area compared to the soft iron piece,the carbon steel piece will dissipate greater heat energy.
$(c)$ This statement means that the state of magnetization of a ferromagnet depends on its history of magnetization. Because the material retains some magnetization even after the external field is removed (retentivity),it can 'remember' the direction of the previously applied magnetic field. This property allows the material to store binary information (bits) based on its magnetic state.
$(d)$ Ceramic ferromagnetic materials (ferrites) are typically used for coating magnetic tapes in cassette players and for building memory stores in computers because they have high resistivity and low eddy current losses.
$(e)$ $A$ region of space can be shielded from magnetic fields by surrounding it with a high-permeability material like soft iron. The magnetic field lines are diverted through the high-permeability material,effectively creating a 'magnetic shield' that leaves the interior region field-free.