Electric Charge and Electromagnetism

• Electromagnetism is one of the four fundamental forces of nature
• The electromagnetic force is responsible for the interactions between charged particles
• It manifests itself through electromagnetic fields, such as electric fields, magnetic fields, and light

Electric Charge

• Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field
• There are two types of electric charge: positive and negative
• Like charges repel each other, and opposite charges attract each other
• The SI unit of electric charge is the coulomb (C)
• Elementary charge, denoted as e, is the electric charge carried by a single proton or electron
• A proton has a charge of +e, and an electron has a charge of -e
• The value of e is approximately 1.602 × 10^-19 C
• Charge is quantized, meaning it exists in integer multiples of the elementary charge
• Electric charge is conserved, the total electric charge in an isolated system remains constant

Coulomb's Law

• Coulomb's Law quantifies the electrostatic force between two charged particles
• The force is directly proportional to the product of the magnitudes of the charges
• The force is inversely proportional to the square of the distance between their centers
• The force acts along the line joining the two charges
• Coulomb's Law: F = k * (|q1 * q2| / 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 × 10^9 N⋅m^2/C^2

Electric Field

• An electric field is a vector field that surrounds an electric charge and exerts a force on other charges within the field
• The electric field is defined as the force per unit positive charge
• The electric field E at a point is given by: E = F / q
• F is the force experienced by a test charge q at that point
• Electric field lines are used to visualize electric fields
• Electric field lines originate from positive charges and terminate on negative charges
• The density of electric field lines indicates the strength of the electric field
• The electric field due to a point charge q at a distance r is given by: E = k * (q / r^2)

Electric Potential

• Electric potential (also called voltage) is the electric potential energy per unit charge
• The electric potential difference between two points is the work done per unit charge to move a charge between those points
• The SI unit of electric potential is the volt (V), where 1 V = 1 J/C
• Electric potential is a scalar quantity
• The electric potential due to a point charge q at a distance r is given by: V = k * (q / r)
• Equipotential surfaces are surfaces where the electric potential is constant
• Electric field lines are always perpendicular to equipotential surfaces

Capacitance

• Capacitance is a measure of a capacitor's ability to store electric charge
• A capacitor typically consists of two conductors separated by an insulator (dielectric)
• The capacitance C is defined as the ratio of the charge Q stored on each conductor to the potential difference V between the conductors: C = Q / V
• The SI unit of capacitance is the farad (F)
• For a parallel-plate capacitor with area A, separation d, and permittivity ε, the capacitance is given by: C = ε * (A / d)
• Capacitors can be connected in series or parallel to achieve different equivalent capacitances
• The energy stored in a capacitor is given by: U = (1/2) * C * V^2 = (1/2) * Q * V = (1/2) * (Q^2 / C)

Electric Current

• Electric current is the rate of flow of electric charge through a conductor
• The SI unit of electric current is the ampere (A), where 1 A = 1 C/s
• Current is conventionally defined as the flow of positive charge, even though in most conductors, it is electrons (negative charge) that are moving
• The direction of conventional current is opposite to the direction of electron flow
• Drift velocity is the average velocity of charge carriers in a conductor due to an electric field

Resistance

• Resistance is a measure of a material's opposition to the flow of electric current
• The SI unit of resistance is the ohm (Ω), where 1 Ω = 1 V/A
• Ohm's Law states that the voltage V across a conductor is proportional to the current I flowing through it: V = I * R
• R is the resistance of the conductor
• Resistivity (ρ) is an intrinsic property of a material that quantifies how strongly it opposes the flow of current
• The resistance R of a wire with length L and cross-sectional area A is given by: R = ρ * (L / A)

Electric Power

• Electric power is the rate at which electrical energy is transferred or consumed in a circuit
• The SI unit of power is the watt (W), where 1 W = 1 J/s
• Electric power P can be calculated using the following formulas:
• P = V * I (Power = Voltage × Current)
• P = I^2 * R (Power = Current^2 × Resistance)
• P = V^2 / R (Power = Voltage^2 / Resistance)

Magnetism

• Magnetism is a phenomenon by which materials exert attractive or repulsive forces on each other
• These forces are due to the motion of electric charges
• Magnetic fields are produced by moving electric charges, electric currents, and magnetic materials
• Magnets have two poles, called the north pole and the south pole
• Like poles repel each other, and opposite poles attract each other
• Earth has its own magnetic field

Magnetic Field

• A magnetic field is a vector field that exerts a force on moving electric charges and magnetic dipoles
• The SI unit of magnetic field strength is the tesla (T)
• Magnetic field lines are used to visualize magnetic fields
• Magnetic field lines form closed loops, unlike electric field lines
• The magnetic field produced by a long, straight wire carrying a current I at a distance r is given by: B = (μ0 * I) / (2πr)
• μ0 is the permeability of free space, approximately 4π × 10^-7 T⋅m/A
• The magnetic force on a moving charge q with velocity v in a magnetic field B is given by: F = q * (v × B)
• The force is perpendicular to both the velocity and the magnetic field

Magnetic Force on Current-Carrying Wires

• A current-carrying wire in a magnetic field experiences a force
• The magnetic force on a straight wire of length L carrying a current I in a magnetic field B is given by: F = I * (L × B)
• The direction of the force is given by the right-hand rule

Electromagnetic Induction

• Electromagnetic induction is the phenomenon in which a changing magnetic field induces an electromotive force (EMF) in a circuit
• Faraday's Law of Induction states that the induced EMF in a closed circuit is equal to the negative rate of change of the magnetic flux through the circuit
• Mathematically, Faraday's Law is: EMF = - dΦ / dt
• Φ is the magnetic flux, defined as the integral of the magnetic field B over the area A of the circuit: Φ = ∫ B ⋅ dA
• Lenz's Law states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it

Inductance

• Inductance is a measure of an inductor's ability to store energy in a magnetic field when an electric current flows through it
• An inductor is typically a coil of wire
• The inductance L is defined as the ratio of the magnetic flux linkage to the current I: L = Φ / I
• The SI unit of inductance is the henry (H)
• The induced EMF in an inductor is given by: EMF = - L * (dI / dt)
• The energy stored in an inductor is given by: U = (1/2) * L * I^2

Maxwell's Equations

• Maxwell's Equations are a set of four fundamental equations that describe the behavior of electric and magnetic fields
• Gauss's Law for Electricity relates the electric field to the electric charge distribution
• Gauss's Law for Magnetism states that there are no magnetic monopoles
• Faraday's Law of Induction relates a changing magnetic field to an induced electric field
• Ampère-Maxwell's Law relates a magnetic field to an electric current and a changing electric field
• Maxwell's Equations demonstrate that electric and magnetic fields are interconnected and can generate each other
• They predicted the existence of electromagnetic waves that travel at the speed of light