Global Journal of Science Frontier Research, A: Physics and Space Science, Volume 22 Issue 1

the air gap is uniform, so it is not necessary to take into account the marginal effects. The following equation is derived from Maxwell's equations and it is also based on the previous assumptions (Clarke, 2021): (8) b) Magnetic domains When materials that exhibit magnetic behaviour are in the presence of magnetic fields, structures called magnetic domains are formed within them, where different groups of magnetic moments align in such a way that they do not cancel each other out. When all or a large majority of the domains are directed in the same direction, the object becomes magnetized in that direction and it becomes a magnet. This is because the magnetic field exerts a torque that tends to align the magnetic moment ( μ ) with itself, which represents the smallest energy configuration such that the vector μ is parallel to the magnetic field lines and perpendicular to the current loop. Thus, the torque is given by the cross product of the magnetic field and μ , which in turn gives the characteristics of a current-carrying spiral such as its current and cross-sectional area. Importantly, the μ of an object is provided by the intrinsic magnetic moment of the electron spin and the magnetic dipole of the electron orbits. The process in which an object is magnetized is called induction and once an object has been induced, it will produce its own magnetic field as long as its dipoles stay aligned. In contrast, an electromagnet remains magnetized only when a current passes through it. In particular, ferromagnetic materials such as iron, nickel and cobalt can become permanent magnets, that is, they will remain magnetized even after being removed from a magnetic field, but they can also present spontaneous magnetization below a temperature critical known as Curie temperature. In general, the Curie temperature for different materials is that at which a material loses its magnetic properties although in most cases it can be replaced by magnetic induction. This is because electrons have higher energies at higher temperatures, which is why the alignment of the magnetic domains is disturbed (Nave, 2021). c) Effect of temperature on resistance Increasing the temperature of a material alters its electrical resistance depending on whether it is a conductor or an insulator. In the case of most conductors, because of their significant number of free electrons, an increase in temperature generates a greater number of collisions between electrons, atoms, and impurities. This hinders the electrical flow, which is equivalent to an increase in resistance and, therefore, the material is said to have a positive temperature coefficient. On the other hand, insulators tend to experience a decay of resistance since having a low number of free electrons means that there are not as many collisions between them and the vibration, caused by the increase in kinetic energy, releases electrons. First, the relationship between a certain physical property M and temperature is determined by: (9) Where delta M is the change in resistance, delta T is the temperature change, and α is the temperature coefficient of resistance. The expression indicates that the fractional change of the variable M is proportional to the product of the temperature and the coefficient already mentioned. The temperature coefficient indicates how much a physical property increases or decreases with the change in temperature (Nave, 1999). Rewriting (8) by decomposing Δ M into M - M ₒ , and Δ T into T - T ₒ , we obtain: (9) The terms are rearranged: (11) Thus, the temperature-dependent physical property is resistivity, which is constant under certain conditions and which determines the strength of material to material given the cross-section and length of the object. In certain cases, it is more convenient to use the inverse of resistivity, called conductivity. It is important to note that increasing the cross-section of an object decreases its resistance since there is more space for the electrons to flow with fewer collisions. On the other hand, increasing its length causes an increase in resistance since the electric potential is "diluted" over a greater distance, causing the speed of the electrons to be lower. Therefore, the resistance is directly proportional to the length and inversely proportional to the cross-section, as shown in the following expression: (12) If one wants to find how the resistivity varies with temperature, one should substitute ρ in place of R and the following remains: (13) In a graphical representation of this phenomenon, resistivity is placed on the y- axis, as the dependent variable, and temperature on the x- axis with the coefficient α being the slope of the graph. At room temperature, the curve is linear and the increase in Relationship between Temperature and the Holding Force of an Electromagnet in a Changing Magnetic Field 1 Year 2022 13 © 2022 Global Journals Global Journal of Science Frontier Research Volume XXII Issue ersion I VI ( A ) M = Mₒ(1+ α (T - Tₒ)) ρ = ρₒ(1 + α (T - Tₒ))