Understanding Electromagnetism

• Electromagnetism is one of the four fundamental forces of nature.

Fundamental Concepts

• Electromagnetism encompasses both electric and magnetic phenomena, which are inseparable and related to moving electric charges.
• Electric charge is a fundamental property of matter that can be positive or negative.
• Like charges repel, and opposite charges attract.
• Electric current is the flow of electric charge.
• Magnetic fields are created by moving electric charges or electric currents.
• Electromagnetic force is mediated by photons, which are massless particles.

Electric Fields

• Electric field is a vector field that exists in the space around electric charges, exerting a force on other charges within the field.
• Electric field lines are used to visualize electric fields, showing the direction of the force on a positive test charge.
• Electric potential is the electric potential energy per unit charge at a specific location in an electric field, measured in volts (V).

Coulomb's Law

• Coulomb's Law quantifies the force between two point charges: ( F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} ), where:
  • ( F ) is the electrostatic force.
  • ( k ) is Coulomb's constant (( \approx 8.987 \times 10^9 , \text{N m}^2/\text{C}^2 )).
  • ( q_1 ) and ( q_2 ) are the magnitudes of the charges.
  • ( r ) is the distance between the charges.
• This force is attractive if the charges are of opposite signs and repulsive if the charges are of the same sign.

Magnetism

• Magnetic fields are created by moving electric charges and exert a force on other moving charges.
• Magnetic field lines form closed loops, originating from the north pole and terminating at the south pole of a magnet.
• Magnetic flux is a measure of the quantity of magnetism, being the number of magnetic field lines passing through a surface.
• Magnetic force on a moving charge is given by ( \vec{F} = q(\vec{v} \times \vec{B}) ), where:
  • ( \vec{F} ) is the magnetic force.
  • ( q ) is the charge.
  • ( \vec{v} ) is the velocity of the charge.
  • ( \vec{B} ) is the magnetic field.

Magnetic Materials

• Ferromagnetic materials (e.g., iron, nickel, cobalt) exhibit strong magnetic properties and can be easily magnetized.
• Paramagnetic materials are weakly attracted to magnetic fields.
• Diamagnetic materials are weakly repelled by magnetic fields.

Electromagnetism

• Electromagnetism describes the interaction between electric and magnetic fields.
• Maxwell's equations unify electric and magnetic phenomena.
• Electromagnetic induction occurs when a changing magnetic field induces an electromotive force (EMF) in a conductor.
• Faraday's Law of Induction: The induced EMF in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit (( \mathcal{E} = -\frac{d\Phi_B}{dt} )).
• Lenz's Law: The direction of the induced current is such that it opposes the change in magnetic flux that produces it.

Maxwell's Equations

• Maxwell's equations describe the behavior of electric and magnetic fields, and how they relate to each other as well as to electric charges and currents.
• Gauss's Law for Electricity: Relates the electric field to the distribution of electric charges (( \nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0} )).
• Gauss's Law for Magnetism: States that magnetic monopoles do not exist, meaning magnetic field lines always form closed loops (( \nabla \cdot \mathbf{B} = 0 )).
• Faraday's Law of Induction: Describes how a changing magnetic field creates an electric field (( \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} )).
• Ampère-Maxwell Law: Describes how a magnetic field is generated by an electric current and/or by a changing electric field (( \nabla \times \mathbf{B} = \mu_0\left(\mathbf{J} + \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}\right) )).

Electromagnetic Waves

• Electromagnetic waves are disturbances in electric and magnetic fields that propagate through space.
• These waves are transverse waves, where the electric and magnetic fields are perpendicular to each other and to the direction of propagation.
• Electromagnetic waves travel at the speed of light (( c \approx 3.0 \times 10^8 , \text{m/s} ) in a vacuum).
• The electromagnetic spectrum includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays, differing in frequency and wavelength.

Inductance

• Inductance (L) is the property of a circuit element to oppose changes in current due to the generation of a back EMF.
• The inductance of a coil depends on its geometry (number of turns, area, length) and the permeability of the core material.
• Inductors store energy in a magnetic field.

Capacitance

• Capacitance (C) is the ability of a component or circuit to collect and store energy in the form of an electrical charge.
• Capacitance is measured in farads (F).
• Capacitors store energy in an electric field.

Electric Circuits

• An electric circuit is a closed path through which electric current flows.
• Ohm's Law relates voltage (V), current (I), and resistance (R): ( V = IR ).
• Resistors impede the flow of current and dissipate energy as heat.
• Series circuits: Components are connected end-to-end, so the current is the same through each component.
• Parallel circuits: Components are connected side-by-side, so the voltage is the same across each component.