Tru Physics

Magnetism

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Tru Physics
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Introduction

Magnetism is a physical phenomenon produced by moving electric charge that results in attractive and repulsive forces between objects. It is one aspect of the combined electromagnetic force and shares many similarities with electricity, which is why they are usually thought of together as electromagnetism.

Magnetic Fields and Magnetic Force

Magnetic fields are a vector field surrounding a magnet, electric current, or changing electric field, with the property that the force experienced in the presence of the magnetic field is dependent on the direction of the field. The magnetic field is denoted by \vec{B} and its unit of measurement is the Tesla (T).

The force exerted by a magnetic field on a moving charge is given by the Lorentz force law:

\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})

where q is the charge, \vec{E} is the electric field, \vec{v} is the velocity, and \vec{B} is the magnetic field. The magnetic force on a particle comes from the second term in this equation.

Magnetic Poles and Magnetic Moments

Every magnet possesses two poles, commonly referred to as the North (N) and South (S) poles. Like poles repel each other, and unlike poles attract each other.

A magnetic dipole, the simplest magnetic field source, can be thought of as a tiny loop of current. The magnetic moment of that loop would be the product of the current and the area of the loop. The direction of the magnetic moment would be perpendicular to the loop in the direction given by the right-hand rule.

The magnetic moment of a system measures the strength and direction of its magnetism. The SI units for magnetic moment are A \cdot m^2 (Amperes times meters squared).

Ampere’s Law and Biot-Savart Law

Ampere’s law relates the integrated magnetic field around a closed loop to the electric current passing through the loop. Mathematically, it is written as:

\oint \vec{B} \cdot d\vec{l} = \mu_0I_{\text{enc}}

where \vec{B} is the magnetic field, d\vec{l} is an infinitesimal vector element of a closed curve, I_{\text{enc}} is the total current enclosed by the curve, and \mu_0 is the permeability of free space.

The Biot-Savart law describes the magnetic field set up by a steady current density. For a small current element, Id\vec{l}, the magnetic field at a distance r is given by:

d\vec{B} = \dfrac{\mu_0}{4\pi}\dfrac{Id\vec{l} \times \hat{r}}{r^2}

Ferromagnetism and Magnetic Materials

Ferromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished, including: ferromagnetism, paramagnetism, and diamagnetism.

Magnetic Flux and Faraday’s Law of Induction

Magnetic flux is the measure of the total magnetic field which passes through a given area. It is defined by the surface integral:

\Phi_B = \int \vec{B} \cdot d\vec{A}

Faraday’s law of induction states that the electromotive force (EMF) induced in any closed circuit is equal to the rate of change of the magnetic flux through the circuit. This can be written as:

\epsilon = -\dfrac{d\Phi_B}{dt}

Maxwell’s Equations and Electromagnetism

Maxwell’s equations are a set of four fundamental equations that govern electromagnetism. They describe the relationship between electric and magnetic fields, as well as how these fields are generated by electric charges and currents. The equations are as follows:

  1. Gauss’s law for electricity: \nabla \cdot \vec{E} = \dfrac{\rho}{\epsilon_0}
  2. Gauss’s law for magnetism: \nabla \cdot \vec{B} = 0
  3. Faraday’s law of induction: \nabla \times \vec{E} = -\dfrac{\partial \vec{B}}{\partial t}
  4. Ampere’s law with Maxwell’s addition: \nabla \times \vec{B} = \mu_0\vec{J} + \mu_0\epsilon_0\dfrac{\partial \vec{E}}{\partial t}

Here, \vec{E} is the electric field, \vec{B} is the magnetic field, \rho is the charge density, \epsilon_0 is the vacuum permittivity, \mu_0 is the vacuum permeability, and \vec{J} is the current density.

These equations form the foundation of classical electromagnetism and explain various phenomena, including the propagation of light and electromagnetic waves.

Applications of Magnetism

Magnetism has many practical applications in modern technology, such as in the design of electric motors and generators, transformers, magnetic storage devices, and magnetic levitation trains. Additionally, magnetic fields are used in medical imaging techniques like magnetic resonance imaging (MRI), which relies on the interaction of magnetic fields with the nuclei in the human body to generate detailed images of internal structures.

Magnetism is a fundamental physical phenomenon that is closely related to electricity. The understanding of magnetic fields and their interactions with charges and currents is essential for the development of various technologies and devices that have become integral to modern society.

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