Magnetic Fields and Materials: Properties and Applications
Magnetic Hysteresis
Magnetic hysteresis occurs when a ferromagnetic material is subjected to a changing magnetic field. As the external field increases and then decreases to zero, the magnetization of the material follows a different path, forming a loop. This loop represents the energy lost due to hysteresis.
Action of a Magnetic Field on a Current
When a conductor carrying an electric current is placed within a magnetic field, a voltage is induced across the conductor’s ends, and a force acts upon it. This force can be calculated using the formula F = B * L * I, where F is the force in Newtons, B is the magnetic field strength, L is the length of the conductor, and I is the current. The direction of the force can be determined using the “right-hand rule”.
Electromagnetic Induction
Electromagnetic induction is the phenomenon where a voltage is produced across a conductor moving through a magnetic field, cutting the magnetic field lines perpendicularly.
Faraday’s Law
Faraday’s Law describes electromagnetic induction in two ways:
- When a conductor moves in a magnetic field perpendicular to the field lines, a voltage is induced. This voltage can be calculated as E = B * L * V, where E is the induced voltage, B is the magnetic field strength, L is the length of the conductor, and V is the velocity.
- When a loop moves perpendicularly through a magnetic field, a voltage is induced that is proportional to the rate of change of magnetic flux through the loop. This can be expressed as E = ΔΦ / Δt, where ΔΦ is the change in magnetic flux and Δt is the change in time.
Lenz’s Law
Lenz’s Law states that the voltage induced in a conductor is such that the resulting current creates a magnetic field that opposes the change in the original magnetic field. The direction of the induced current can be determined using the “right-hand rule” from V to B.
Losses in Iron Cores
In DC circuits, there are no iron losses. However, in AC circuits, the current varies with time, causing the magnetic flux to change in magnitude. This leads to heating of the ferromagnetic material due to the friction of its magnetic particles.
Eddy Currents
Eddy currents are currents induced in the iron core due to the variation of magnetic flux. To minimize eddy currents, laminated iron cores are used, where thin sheets of metal are insulated from each other, reducing the area available for current flow.
Hysteresis Loss
Hysteresis loss refers to the energy lost due to the friction of magnetic molecules as they are reoriented during each hysteresis loop. This loss can be reduced by decreasing the frequency of the alternating current or by using materials with a smaller hysteresis loop area.
Self-Induction and Coils
Self-induction is the phenomenon where a changing current in a coil induces a voltage in the coil itself. This induced voltage opposes the change in current, causing the current to increase or decrease more slowly. Inductance (L), measured in Henries, is the ratio of the induced voltage to the rate of change of current (L = V / (ΔI/Δt)).
Molecular Theory of Magnets
Ferromagnetic materials are composed of magnetic molecules. In non-magnetic materials, these molecules are randomly oriented. In magnets, a body capable of attracting ferromagnetic materials, the magnetic molecules are all aligned. Magnets can be natural (like magnetite) or artificial. Artificial magnets can be demagnetized by heat or by mechanical shock.
Electromagnets
Electromagnets are created by passing an electric current through a conductor, generating a magnetic field around it.
Magnetic Field Created by a Current-Carrying Conductor
When a current flows through a conductor, circular magnetic field lines are formed around it. The direction of these field lines can be determined using the “right-hand rule”.
Magnetic Field Created by a Loop
When a current flows through a loop of wire, the magnetic field lines add up, creating a stronger field. The direction of this field can be found using the “right-hand rule”.
Magnetic Field Produced by a Coil
When a coil is wrapped around a ferromagnetic core, the magnetic field lines from each turn of the coil combine, creating a much more intense magnetic field. The direction of this field can be determined using the “right-hand rule”.
Magnetic Induction
Magnetic induction (B) measures the strength of a magnetic field and is represented in Tesla (T). Magnetic flux is the product of the magnetic field strength and the cross-sectional area.
Magnetization Curve
The magnetic field of a coil is proportional to the magnetic field intensity and is constant for all coils (B0 = μ0 * H).
Magnetic Permeability
Relative permeability (μr) is the number of times a magnetic field is increased by placing a ferromagnetic material inside the coil (B = μr * B0).