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

II. T heoretical F ramework a) Faraday's Law If a coil of wire is in a changing magnetic field, an electric current will be induced in the wire. This happens because any change in a magnetic field, either in its magnitude, the magnitude of the surface vector, in the position of a conductor with respect to it, or its direction, originates an electric field and an electromagnetic force. However, this term has been reduced to emf ( ) because it is not a force but a voltage. This phenomenon is described by Faraday’s law, which succinctly summarizes how the emf can vary by establishing that it is proportional to the rate of change in the magnetic flux. In turn, the magnetic flux is a measurement of the total magnetic field that passes through a certain area and can also be defined as the number of magnetic field lines per unit area (Haus et al., 2008). Although the concept of emf and voltage are similar, no charge separation is required for the former to be generated. The direction of the induced current can be determined from Lenz's Law, which indicates that the polarity of the emf is such that it induces a current whose magnetic field opposes the change in the magnetic field that generated it in the first instance. In the specific case of a current-carrying coil of wire, if the geometry of the coil is kept fixed, the change in magnetic flux will depend on variations in current. The tendency of the coil or any type of electrical conductor to oppose a certain change in current is quantified with the property known as inductance, defined by the symbol L. Thus, inductance is also defined as the ratio between the voltage and the ratio change of current, and its unit is the henry (H): (1) Thus, if the winding has an area A , length l , a number of turns N , and is in a magnetic flux B , the emf ε is: (2) bulge when they pass through non-magnetic materials such as air, thus producing an inhomogeneous magnetic field. But if the diameter of the solenoid is much smaller than its length, it can be considered infinitely long so as to simplify calculations (Nave, 2021). Using Ampère's law and the previously mentioned approximation, the expression for the magnetic field of a solenoid is obtained: (3) In (3), μ 0 denotes the permeability of free space, or the property of materials - in this case of a vacuum- to allow the formation of magnetic fields. Therefore (2) is rewritten as: (4) When entering (4) in (2), the result is: (5) However, if a magnetic material is introduced into the solenoid, μ 0 will have to be replaced by μ , the permeability of the core and hence, its inductance increases. Since the relative permeability is the quotient between μ and μ 0 , the following statements are equivalent: (6) (7) To find the force produced by a coil's magnetic field, it is necessary to understand how the energy associated with it changes. For conservation of energy, the energy required to push current through a conductor must have an outlet. For an inductor, this output is the magnetic field. Now, in an electromagnet with varying current, such as the one that is being analyzed in the present work, it is important to consider the power required to push the current through the conductor against the voltage induced by the change in the magnetic flux. The calculations can be simplified under the assumption that all electrical energy is converted into the energy of the magnetic field and consequently, the effects of eddy currents, which dissipate energy in the form of heat, are ignored. In addition, if the air gap of the electromagnet is small compared to its cross- sectional area, it can be assumed that the field within Relationship between Temperature and the Holding Force of an Electromagnet in a Changing Magnetic Field © 2022 Global Journals 1 Year 2022 12 Global Journal of Science Frontier Research Volume XXII Issue ersion I VI ( A ) The magnetic field in any closed path is calculated from Ampère's circuit law, which states that the product of the elements of length and the intensity of the induced magnetic field in the surrounding space is proportional to the current flowing through the loop. In the idealized case of an infinitely long solenoid, the magnetic field is homogeneous along almost its entire length, only with the exception of its ends; thus, the bulging of the magnetic field lines at the ends can be ignored, a phenomenon also known as the marginal effect (Bae et al., 2009). This effect is observed because the magnetic field lines repel each other and, therefore, ε