Definition of Ferromagnetic Materials:
- Ferromagnetic materials are substances that exhibit strong magnetization when placed in an external magnetic field.
- These materials retain their magnetization even after the external field is removed.
- Common examples include iron (Fe), cobalt (Co), and nickel (Ni). Explanation of Ferromagnetism:
- The phenomenon of ferromagnetism arises due to the presence of magnetic domains.
- Each domain consists of a group of atomic dipoles aligned in the same direction.
- In an unmagnetized ferromagnetic material, these domains are randomly oriented, resulting in zero net magnetization.

Magnetic Domains and Alignment:
- When an external magnetic field is applied, the domains align in the direction of the field.
- The material becomes magnetized, and the alignment of the domains increases the overall magnetic moment. \[ B = \mu_0 (H + M) \] where:
- \( B \) = Magnetic field in the material
- \( H \) = Applied external field
- \( M \) = Magnetization of the material
- \( \mu_0 \) = Permeability of free space - In fully magnetized ferromagnetic materials, most domains align in the same direction, producing a strong magnetic effect.
Key Properties of Ferromagnetic Materials:
1. High Permeability: These materials have a high ability to concentrate magnetic flux.
2. Hysteresis Effect: The magnetization does not return to zero immediately after removing the field, leading to a hysteresis loop.
3. Curie Temperature (\( T_C \)): Above this temperature, the material loses its ferromagnetic properties and behaves as a paramagnet.
Conclusion:
- Ferromagnetic materials are widely used in applications like transformers, electromagnets, hard disks, and electric motors due to their ability to retain strong magnetization.
Two long parallel wires X and Y, separated by a distance of 6 cm, carry currents of 5 A and 4 A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance of 4 cm from wire Y is \( 3 \times 10^{-5} \) T. The value of \( x \), which represents the distance of point P from wire X, is ______ cm. (Take permeability of free space as \( \mu_0 = 4\pi \times 10^{-7} \) SI units.) 
A particle of charge $ q $, mass $ m $, and kinetic energy $ E $ enters in a magnetic field perpendicular to its velocity and undergoes a circular arc of radius $ r $. Which of the following curves represents the variation of $ r $ with $ E $?
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If oxygen ion (O\(^{-2}\)) and Hydrogen ion (H\(^{+}\)) enter normal to the magnetic field with equal momentum, then the path of O\(^{-2}\) ion has a smaller curvature than that of H\(^{+}\).
Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.
In the light of the above statements, choose the correct answer from the options given below
