Electromagnetism and Electric Charge

• Electromagnetism is a fundamental force of nature, and is the interaction of electric and magnetic fields
• Electromagnetism encompasses the electric force and the magnetic force
• In electromagnetism, charged particles interact with electromagnetic fields
• Electromagnetism underlies the properties of light

Electric Charge

• Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field
• Electric charge is quantized, meaning it exists in discrete units
• The elementary unit of charge is the charge of a single electron or proton, denoted as e ≈ 1.602 × 10⁻¹⁹ coulombs
• There are two types of electric charge: positive and negative
• Like charges repel each other, and opposite charges attract each other.
• Electric charge is conserved, meaning the total electric charge in an isolated system remains constant

Electric Field

• An electric field is a vector field that exists in the space surrounding an electric charge
• The electric field exerts a force on other charged objects within the field
• The electric field is defined as the electric force per unit positive charge
• The electric field E at a point in space is given by E = F/q, where F is the electric force experienced by a small positive test charge q at that point
• The electric field lines are used to visualize the electric field
• Electric field lines point away from positive charges and toward negative charges
• The density of electric field lines indicates the strength of the electric field

Coulomb's Law

• Coulomb's Law quantifies the electrostatic force between two point charges
• The electrostatic force is directly proportional to the product of the magnitudes of each charge
• The electrostatic force is inversely proportional to the square of the distance between the charges
• The electrostatic force acts along the line joining the two charges
• Mathematically, Coulomb's Law is expressed as F = k * (|q1q2| / r²)
• F is the electrostatic force
• q1 and q2 are the magnitudes of the charges
• r is the distance between the charges
• k is Coulomb's constant, approximately 8.9875 × 10⁹ N⋅m²/C²

Electric Potential

• Electric potential, also known as voltage, is the electric potential energy per unit charge at a specific location in an electric field
• Electric potential is a scalar quantity, measured in volts (V)
• The electric potential difference between two points is the work required to move a unit positive charge from one point to the other
• The electric potential V at a point is given by V = U/q, where U is the electric potential energy of a charge q at that point
• The electric field is related to the gradient of the electric potential E = -∇V
• Equipotential surfaces are surfaces on which the electric potential is constant

Capacitance

• Capacitance is the ability of a body to store electrical energy in the form of an electric field
• Capacitance is defined as the ratio of the change in electric charge of a system to the corresponding change in its electric potential
• A capacitor is a device designed to store electrical energy
• Capacitance C is given by C = Q/V, where Q is the charge stored on the capacitor and V is the voltage across the capacitor
• The unit of capacitance is the farad (F)
• The energy U stored in a capacitor is given by U = (1/2)CV²

Electric Current

• Electric current is the rate of flow of electric charge through a conductor
• Electric current is measured in amperes (A)
• One ampere is defined as one coulomb of charge passing a given point per second
• Electric current is typically due to the flow of electrons in a conductor
• Conventional current direction is defined as the direction of positive charge flow
• Drift velocity is the average velocity of charge carriers in a conductor due to an electric field

Resistance

• Resistance is the opposition to the flow of electric current in a material
• Resistance is measured in ohms (Ω)
• Ohm's Law states that the voltage V across a conductor is directly proportional to the current I flowing through it: V = IR
• R is the resistance of the conductor
• Resistivity is the measure of a material's resistance to electric current for a given size and shape
• The resistance R of a wire is given by R = ρ(L/A)
• ρ is the resistivity of the material
• L is the length of the wire
• A is the cross-sectional area of the wire

Electric Circuits

• An electric circuit is a closed path through which electric current can flow
• Circuits contain components such as resistors, capacitors, inductors, voltage sources, and current sources
• Series circuits have components connected end-to-end
• The current is the same through each component in a series circuit
• Parallel circuits have components connected side-by-side
• The voltage is the same across each component in a parallel circuit
• Kirchhoff's current law (KCL) states that the total current entering a junction is equal to the total current leaving the junction
• Kirchhoff's voltage law (KVL) states that the sum of the voltage drops around any closed loop in a circuit is zero

Magnetic Field

• A magnetic field is a vector field that surrounds a magnetic material or a moving electric charge
• The magnetic field exerts a force on other magnetic materials or moving charges within the field
• Magnetic field lines are used to visualize the magnetic field
• Magnetic field lines form closed loops and point from the north pole to the south pole outside a magnet
• The magnetic field is measured in teslas (T)
• Sources of magnetic fields include permanent magnets, electric currents, and changing electric fields

Magnetic Force

• A moving charge experiences a force in a magnetic field
• The magnetic force F on a charge q moving with velocity v in a magnetic field B is given by F = q(v × B)
• The magnetic force is perpendicular to both the velocity of the charge and the magnetic field
• The magnetic force does no work on the charge; it only changes the direction of the velocity
• A current-carrying wire in a magnetic field experiences a magnetic force
• The magnetic force F on a wire of length L carrying current I in a magnetic field B is given by F = I(L × B)

Ampère's Law

• Ampère's Law relates the magnetic field around a closed loop to the electric current passing through the loop
• Ampère's Law states that the line integral of the magnetic field B around a closed loop is proportional to the current I enclosed by the loop: ∮ B ⋅ dl = μ₀I
• μ₀ is the permeability of free space, approximately 4π × 10⁻⁷ T⋅m/A
• Ampère's Law is used to calculate the magnetic field produced by symmetric current distributions

Faraday's Law

• Faraday's Law of Induction describes how a changing magnetic field creates an electromotive force (EMF)
• The EMF is the voltage induced in a circuit due to a changing magnetic field
• The magnitude of the EMF is proportional to the rate of change of the magnetic flux through the circuit
• Faraday's Law is expressed as EMF = -N (dΦB / dt)
• N is the number of turns in the coil
• ΦB is the magnetic flux through the coil
• The negative sign indicates the direction of the induced EMF opposes the change in magnetic flux (Lenz's Law)

Inductance

• Inductance is a measure of a coil's ability to oppose changes in current
• Inductance is defined as the ratio of the induced voltage to the rate of change of current
• An inductor is a circuit component designed to have a specific inductance
• The inductance L is given by L = NΦB / I
• N is the number of turns
• ΦB is the magnetic flux through the inductor
• I is the current flowing through the inductor
• The unit of inductance is the henry (H)
• The energy U stored in an inductor is given by U = (1/2)LI²

Electromagnetic Waves

• Electromagnetic waves are disturbances that propagate through space by the interaction of electric and magnetic fields
• Electromagnetic waves are generated by accelerating electric charges
• Electromagnetic waves are transverse waves, meaning the electric and magnetic fields are perpendicular to the direction of propagation
• Electromagnetic waves travel at the speed of light in a vacuum, denoted as c ≈ 3.0 × 10⁸ m/s
• The speed of light c is related to the permeability μ₀ and permittivity ε₀ of free space by c = 1 / √(ε₀μ₀)
• The electromagnetic spectrum includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays
• Electromagnetic waves carry energy and momentum
• The energy flux (power per unit area) of an electromagnetic wave is given by the Poynting vector S = (1/μ₀)(E × B)