Electricity

Electricity encompasses physical phenomena involving electric charge. The core concepts of electricity include the effects of static charges (electric fields and potentials) and the dynamics of moving charges (electric current and circuits). These concepts are fundamental to various diagnostic tools and treatments (e.g., ECGs, defibrillators) and to understanding biological processes such as nerve impulse conduction. This article covers the foundational principles of electrostatics, electrodynamics, and the effect of magnetic fields on charges. See “Resting potentials and action potentials” for information on nerve impulses.

Electric charge is a fundamental property of elementary particles (such as electrons and quarks) that determines their interactions with electric and magnetic fields.

Electric charge

• Symbol: Q or q
• Unit: coulomb (C)
• Properties
  • Positive or negative
    • Charges with the same sign repel each other.
    • Charges with opposite signs attract each other.
  • Quantized: Its value is an integer multiple of the elementary charge (e = 1.6 × 10^-19 C).
• Law of conservation of charge: In a closed system, the total electric charge must remain constant.
• Coulomb's law: a fundamental principle of electrostatics that quantifies the magnitude of force between two stationary point charges
  • Formula: F = (k × q₁ × q₂)/r²
    • Unit: newton (N)
    • F = electrostatic force (N), q₁ and q₂ = point charges (C), r = distance between the two charges (m), k = Coulomb's constant (k ≈ 9 × 10⁹ N⋅m²/C²); also written as k = 1 / (4πɛ0), where ɛ0 is the permittivity of free space (approximately 8.85 × 10^-12 C²/N⋅m²)
  • Concept: The force is repulsive for like charges (+/+ or -/‑) and attractive for opposite charges (+/‑); the strength of this force varies depending on the magnitude of the charges and the distance between them.

Like charges repel, opposite charges attract.

The sum of charges in a closed system always remains constant.

Coulomb's law states that the force increases with greater amounts of charge and decreases as the distance between the charges increases.

Classification of materials

Materials can be broadly classified by their ability to transmit electric charge.

• Conductors
  • Materials containing movable charges (e.g., delocalized electrons in metals, ions in electrolytic solutions or plasma) that permit the flow of electric current
  • E.g., used to carry electrical current through wires
• Insulators
  • Materials in which internal charges are not free to move and thus do not conduct electricity
  • A dielectric is a special type of insulator that can become polarized in an electric field, which is a key property for capacitors.
  • E.g., plastic or rubber used as a coating for wires

Conductors allow current flow, while insulators block it.

Electric field

Electric charges generate electric fields in the space around them. These fields exert a Coulomb force on any other nearby charges. Electric fields are visualized using field lines, which indicate the direction and strength of the force.

• Formulas
  • Electric field strength from force for uniform and non-uniform fields: E = F/q
    • Unit: newton per coulomb (N/C)
    • E = electric field strength (N/C), F = Coulomb force (N), q = magnitude of the test charge (C)
  • For a uniform field (e.g., between capacitor plates): E = V/d
    • Unit: volt per meter (V/m)
    • E = electric field strength (V/m), V = voltage (V), d = distance (m)
• Field properties
  • The net electric field at a given point is the vector sum of the fields from each source charge.
  • A charge in the field experiences a force: Positive charges are pushed in the field's direction (i.e., toward the negative pole), while negative charges are pushed in the opposite direction (i.e., toward the positive pole).
• Electric field lines
  • Properties
    • Direction: Lines originate on positive charges and terminate on negative charges, showing the path of a positive test charge.
    • Strength: The density of the lines indicates field strength; the closer the lines, the stronger the field.
    • Behavior: Field lines never cross. In a uniform field, field lines are parallel and equally spaced, and the electric field strength is the same at every point.
• Dielectric constant (κ or ε_r): a dimensionless measure that indicates a material's ability to store electrical energy in an electric field compared to a vacuum
  • Formulas
    • κ = E₀/E
      • Unit: dimensionless
      • κ (or ε_r) = dielectric constant (unitless), E₀ = field strength in a vacuum (V/m), E = net field strength in the dielectric material (V/m), F = force (N), F₀ = force in a vacuum (N)
    • κ = F₀/F
      • Unit: dimensionless
      • κ (or ε_r) = dielectric constant (unitless), F₀ = force in a vacuum (N), F = force in the dielectric (N)
  • Concept: When placed in an external electric field, the molecules within the dielectric become polarized (positive charges shift in the direction of the field and negative charges shift against it). This creates an internal electric field that opposes the external field. Materials with a high dielectric constant are effective at storing energy in capacitors.

The dielectric constant indicates how much electric field energy a material can store compared to a vacuum. A higher dielectric constant means the material can store more energy, which is crucial in various applications, such as capacitors used in electronic devices and medical equipment.

Electric potential and electric potential energy describe the energy associated with a charge's position within an electric field.

Electric potential energy (U)

• Definition
  • The stored potential energy of a test charge (q) at a specific position in an electric field
  • It is the work required to bring the charge from a reference point (often considered to be at infinity) to that position.
• Formula for two point charges: U = (k × q₁ × q₂)/r
  • Unit: joule (J)
  • U = potential energy (J), k = Coulomb's constant (N⋅m²/C²), q₁ and q₂ = charges (C), r = distance between charges (m)
• Characteristics
  • Depends on both the position and size of the test charge
  • Positive U for like charges (repulsion requires energy input) and negative U for opposite charges (attraction releases energy)

Electric potential (V)

• Definition
  • The amount of electric potential energy per unit charge at a specific point in space
  • It is a property of the electric field, created by one or more source charges
• Formulas
  • Electric potential at a point: V = U/q₀
    • Unit: volt (V) or joule per coulomb (J/C)
    • V = electric potential (V or J/C), U = potential energy (J), q₀ = test charge to probe the field (C)
  • The electric potential at a distance (r) from a point charge: V = kQ/r
    • V = electric potential (V or J/C), k = Coulomb's constant (N⋅m²/C²), Q = source charge (V or J/C), r = distance between charges (m)
• Characteristics
  • Depends only on the source charge creating the field, not on the test charge (q₀), which must be small enough not to disturb the field
  • Positive source charges create positive potentials and negative source charges create negative potentials.
• Superposition: The total potential at a point is the algebraic sum of the potentials from each source charge.

Potential vs. potential energy: The hill analogy. Think of an electric field as a hilly landscape. Electric potential (V) is like the height of a spot on the hill. A point 100 m up has that height regardless of what's sitting there. It is a property of the location. Electric potential energy (U) is the energy a specific object (e.g., a boulder) has at that height. A heavy boulder has more potential energy at 100 m than a small pebble. It is the energy of the charge at that location.

Electric potential is a way to describe the "potential for energy" that exists at a location in an electric field, while electric potential energy is the actual energy a particular charge has when it is at that location.

Equipotential lines

• Lines connecting points in space that have the same electric potential
• They are always perpendicular to electric field lines.
• No work is done when moving a charge along an equipotential line.

Electric dipole

• A pair of equal and opposite charges separated by a small distance.
• In an electric field, a dipole will experience a torque that aligns it with the field.

Capacitor

• Characteristics
  • A component that stores electric charge and electrical energy in an electric field
  • Consists of two conductive plates separated by a non-conductive dielectric (insulating) material
  • When a voltage is applied across the plates, an electric field forms in the dielectric, storing energy (see “Electric field”).
• Capacitance (C): a measure of a capacitor's ability to store charge at a given voltage
  • Formula: C = Q/V
    • Unit: farad (F)
    • C = capacitance (F), Q = charge (C), V = voltage (V)
  • Parallel plate capacitor : C = ε_r × ε₀ × A/d
    • Unit: farad (F)
    • C = capacitance (F), ε_r = relative permittivity (dielectric constant; unitless), ε₀ = permittivity of free space (F/m), A = area of plates (m²), d = distance between plates (m)
• Energy of a charged capacitor (U_C): the electric potential energy stored in the electric field of a capacitor
  • Formula: U_C = ½ × Q × V = ½ × C × V² = ½ × Q²/C
    • Unit: joule (J)
    • U_C = stored energy (J), Q = charge (C), V = voltage (V), C = capacitance (F)
  • Capacitors in circuits
    • Capacitors in series: 1/C_total = 1/C₁ + 1/C₂ + ...
    • Capacitors in parallel: C_total = C₁ + C₂ + ...
    • C_total = total capacitance of the series circuit (F), C₁ = capacitance of the first capacitor in the series (F), C₂ = capacitance of the second capacitor in the series (F)
• Current in a capacitor: the flow of charge to or from the capacitor plates
  • Formula: I = Q/t
    • Unit: ampere (A)
    • I = current (A), Q = charge (C), t = time (s)
• RC circuits: a circuit containing a resistor and a capacitor
  • Time constant (τ): indicates how quickly a capacitor charges or discharges; a smaller time constant means faster charging/discharging
    • Formula: τ = R × C
      • Unit: second (s)
      • R = resistance (Ω), C = capacitance (F), τ = time for current to reach ∼ 63% of its final value after a change (s)
  • Discharge voltage: The voltage across a discharging capacitor decreases exponentially over time; during discharge, the capacitor acts as a battery to drive current.
    • Formula: V(t) = V₀ × e - (t/RC)
      • Unit: volt (V)
      • V(t) = voltage across the capacitor at time t (V), V₀ = initial voltage across the capacitor at time t = 0 (V), t = time since discharge started (s), R = resistance through which the capacitor discharges (Ω), C = capacitance of the capacitor (F), RC = time constant (τ) of the RC circuit (s), e = Euler’s number, approximately 2.718 (unitless)

Capacitor voltage decays exponentially when discharging.

A defibrillator uses a large capacitor to deliver a powerful shock to the heart to restore a normal rhythm.

Example calculation

A parallel plate capacitor with a plate area of 5 cm², a plate separation of 6 cm, and a dielectric with a constant of 4.5 is connected to a 10 V source. What is the maximum charge that can be stored?

• Find: charge (Q)
• Given: plate area (A), plate separation (d), dielectric constant (ε_r), voltage (V)
  • First, find capacitance (C): C = ε_r × ε₀ × A/d = 4.5 × (8.85 × 10^-12 F/m) × (0.0005 m²/0.06 m) ≈ 0.33 × 10^-12 F
  • Next, find charge (Q): C = Q/V → Q = C × V = (0.33 × 10^-12 F) × 10 V = 3.3 × 10^-12 C

The directed movement of charge constitutes an electric current. The following quantities describe current:

• Electric current (I): the amount of electric charge that flows per unit of time through a point or region
  • Formula: I = Q/t
    • Unit: ampere (A), which is one coulomb per second (C/s)
    • I = current (A), Q = charge (C), t = time (s)
  • Concept: Current describes the total flow of charge carried by particles such as electrons in a wire or ions in a solution.
• Electric voltage (V): the difference in electric potential energy between two points per unit of electric charge
  • Formula: V = W/Q
    • Unit: volt (V), which is one joule per coulomb (J/C)
    • V = voltage (V), W = work (J), Q = charge (C)
  • Concept: Voltage, or potential difference, is the driving force in a circuit. No current flows without a voltage difference.
• Current density: a measure of the concentration of electric current, defined as the amount of current flowing through a unit of cross-sectional area
  • Formula: j = I/A
    • Unit: amperes per square meter (A/m²)
    • j = current density (A/m²), I = current (A), A = cross-sectional area (m²)
  • Concept: While current is a scalar measuring total flow, current density is a vector describing the flow's distribution and direction at a specific point.
• Electrical resistance (R): a measure of the opposition to current flow for a specific object, indicating the voltage required for a certain current to pass through it
  • Formula (Ohm's law): R = V/I
    • Unit: ohm (Ω)
    • R = resistance (Ω), V = voltage (V), I = current (A)
  • Concept: Unlike resistivity (a material property), resistance is a property of an object that depends on its specific material, shape, and size.
• Resistivity (ρ): an intrinsic property of a material that quantifies how strongly it resists the flow of electric current
  • Formulas
    • Resistivity: ρ = R × A/L
    • Resistance of a conductor: R = ρ × L/A
      • R = resistance (Ω), ρ = resistivity (Ω·m), L = length (m), A = cross-sectional area (m²), e.g., a circle with A = π × (diameter/2)² or rectangle with A = length × width
    • Unit: ohm-meter (Ω⋅m)
  • Concept: The formula is used to model the resistance of components such as ECG wires or biological structures such as nerve axons.
• Conductivity (σ): an intrinsic property of a material that quantifies how well it conducts electric current; it is the reciprocal of resistivity
  • Formula: σ = 1/ρ
    • Unit: siemens per meter (S/m)
    • σ = conductivity (S/m), ρ = resistivity (Ω⋅m)
  • Concept
    • Materials with high conductivity (e.g., copper or silver) are good conductors.
    • Materials with very low conductivity (e.g., rubber or glass) are insulators.
• Electrical conductance (G): a measure of how well a specific component or circuit conducts electric current through a specific object or component; it is the reciprocal of resistance
  • Formula: G = 1/R
    • Unit: siemens (S), which is equivalent to 1/Ω
    • G = conductance (S), R = resistance (Ω)
  • Concept: While conductivity (σ) is a property of a material, conductance is a property of a specific component.
    • Components with high conductance allow a large amount of current to flow for a given voltage.
    • Components with low conductance restrict current flow.
• Conduction velocity (v): the average speed at which a charge carrier, such as an electron, moves through a conductor (drift velocity)
  • Formula: v = d/t
    • Unit: meters per second (m/s)
    • v = velocity (m/s), d = distance (m), t = time (s)
  • Concept: Conduction velocity is limited by the medium's resistance (opposition to flow) and capacitance (charge storage). For example, in myelinated neurons, the myelin sheath decreases capacitance, dramatically increasing the action potential's conduction velocity.
• Types of conduction
  • Metallic conduction
    • Delocalized electrons are free to move between positively charged metal ions.
    • Example: current flowing through a copper wire
  • Electrolytic conduction
    • Occurs in ionic solutions (electrolytes) via the movement of ions
      • Cations (positive ions) move toward the negative electrode (cathode).
      • Anions (negative ions) move toward the positive electrode (anode).
    • Concept: This is the primary mechanism for electrical signaling in biological systems (e.g., in the cytoplasm of neurons and muscle cells).
• Factors affecting conductivity
  • Electrolyte concentration: Conductivity is highest at an optimal concentration and decreases if the concentration is too high or too low.
  • Temperature
    • In metals, conductivity decreases as temperature increases.
    • In semiconductors, conductivity increases as temperature increases.

According to Ohm's law (V = IR), voltage (ΔV) is the driving force that pushes an electric current (I), or the flow of charge, against the opposition of resistance (R).

Imagine electric current as a river flowing down a mountain: The volume of water flow corresponds to the electric current, and the change in altitude that drives the flow corresponds to the voltage.

Electric current and fluid flow in the human body share several similarities: both involve the movement of a substance (electrons in electrical circuits and blood in the circulatory system), experience resistance that impacts their flow rate, are influenced by pressure differences (voltage in electrical systems and blood pressure in the circulatory system), and adhere to conservation principles, in which the total electric charge in a circuit remains constant and the total mass of blood in a vessel is conserved.

Electrical conductance should not be confused with electrical conductivity. Conductance refers to how well a specific component conducts electricity, while conductivity is a constant property of the material itself.

Example calculation: conduction velocity

A nerve impulse travels over a distance of 40 cm in 0.03 seconds. What is the conduction velocity?

• Find: conduction velocity (v)
• Given: distance (s), time (t)
  • v = s/t = 0.4 m/0.03 s ≈ 13.3 m/s

Example calculation: current

In a conductor with a cross-section of 16 mm², 6 × 10¹⁸ electrons flow per second. The voltage in the system is 25 V. What is the current density and what is the resistance of the circuit?

• Find: current density (j), resistance (R)
• Given: number of electrons (N_e), time (t), conductor cross-section (A), voltage (V)
  • Q = N_e × e = 6 × 10¹⁸ × (1.6 × 10^-19 C) = 0.96 C
  • I = Q/t = 0.96 C/1 s = 0.96 A
  • j = I/A = 0.96 A/16 mm² = 0.06 A/mm²
  • R = V/I = 25 V/0.96 A ≈ 26 Ω

Electrical work and power

The energy transferred by an electric current is called electrical work. Power is the rate at which electrical work is done.

• Electrical work (W): the energy required to move a charge across a potential difference (voltage) or the energy released when a charge moves along a potential difference
  • Formulas
    • W = V × Q
      • Unit: joule (J), which is one newton-meter (N⋅m) or one volt-coulomb (V⋅C)
      • W = electrical work or energy (J), Q = charge (C), V = voltage (V)
    • Since Q = I × t, it is also expressed as W = V × I × t.
      • Unit: joule (J)
      • W = electrical work or energy (J), Q = charge (C), V = voltage (V), I = current (A), t = time (s)
  • Concept: Electrical work is the total energy consumed by a circuit component (e.g., a resistor) or supplied by a source (e.g., a battery) over a period of time. It is the energy counterpart to power.
• Electrical power (P): the electrical work done per unit of time
  • Formulas
    • P = W/t
      • Unit: watt (W), which is one joule per second (J/s) or one volt-ampere (V⋅A)
      • P = power (W), W = electrical work (J), t = time (s)
    • Using Ohm's law, it is commonly calculated as P = V × I or in its other forms, P = I² × R and P = V²/R.
      • Unit: watt (W)
      • P = power (W), V = voltage (V), I = current (A), R = resistance (Ω)
  • Concept: Power describes instantaneous energy usage. For example, a 100-watt light bulb converts 100 joules of electrical energy into light and heat each second.
• In an electric circuit, power can be calculated using electrical quantities such as voltage, current, and resistance.

Example calculation

A household appliance in standby mode draws a current of 0.5 A. What energy, in the form of electrical work, is consumed in one hour if the device has an impedance (AC resistance) of 12 Ω?

• Find: electrical work (W)
• Given: current (I), impedance (R), time (t)
  • There are several ways to solve this; the method using voltage (V) and power (P) is shown here:
    • V = R × I = 12 Ω × 0.5 A = 6 V
    • P = V × I = 6 V × 0.5 A = 3 W
    • W = P × t = 3 W × 3,600 s = 10,800 J (= 10.8 kJ)

In practice, two types of electric current are used: direct current and alternating current.

Direct current (DC)

• Definition: current in which the positive and negative poles remain constant, so the current always flows in one direction
• Direction of flow: By convention, current flows from positive to negative, but electrons (the charge carriers in metals) flow from the negative to the positive pole.
• Example: a battery

Alternating current (AC)

• Definition: current in which the polarity reverses at a constant frequency
• Direction of flow: The electrons continuously change their direction of flow, oscillating back and forth.
• Example: current from a wall socket
• Mathematical description
  • Sinusoidal voltage: V(t) = V₀ × sin(ωt)
    • Unit: volt (V)
    • V(t) = instantaneous voltage (V), V₀ = peak voltage (V), t = time (s), ω = angular frequency (rad/s)
  • Angular frequency: ω = 2 × π × f = 2 × π/T
    • Unit: radians per second (rad/s)
    • ω = angular frequency (rad/s), f = frequency (Hz), T = period of oscillation (s)
• Effective RMS voltage: the DC voltage that would deliver the same average power as an AC voltage
  • Because voltage and current vary continuously in AC circuits, effective (RMS) values are used for calculations.
  • Formula: Vrms = Vpeak / √2
    • Unit: volt (V)
    • Vrms = root mean square voltage (V), Vpeak = peak voltage reached by the AC waveform (V)

AC is generally more dangerous than DC because its rapid changes in direction can interfere with the heart's rhythm, potentially causing ventricular fibrillation. For this reason, DC is typically considered life-threatening above 120 V, whereas AC is considered life-threatening above 50 V. For details, see “Electrical and lightning injuries.”

Simple circuits

In a circuit, one or more components are connected to a power source by conductors, allowing current to flow between a positive and a negative pole. A simple symbolic notation is used to represent such circuits.

Series and parallel circuits

Components can be connected one after another (in series) or side by side in separate branches (in parallel). Combinations of series and parallel connections are also common. The rules for these circuits have useful analogies to pressure and flow in the bloodstream (see “Vascular physiology”).

Example calculation

Three resistors (R₁ = 20 Ω, R₂ = 25 Ω, R₃ = 18 Ω) are installed in a circuit. Determine the total resistance for a series circuit and for a parallel circuit.

• Find: total resistance (R_total)
• Given: individual resistances (R₁, R₂, R₃), circuit type
  • Series circuit: R_total = R₁ + R₂ + R₃
    • 20 Ω + 25 Ω + 18 Ω = 63 Ω
  • Parallel circuit: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃
    • 1/R_total = 1/20 Ω + 1/25 Ω + 1/18 Ω ≈ 0.146 Ω^-1
    • R_total ≈ 1/0.146 Ω^-1 ≈ 6.85 Ω

Kirchhoff's laws

Junction rule (first law)

The total current flowing into a junction must equal the total current leaving the junction. This is a statement of conservation of charge.

Loop rule (second law)

• Principle: For any closed loop in a circuit, the sum of all voltages around the loop is zero. This is a statement of conservation of energy.
  • ΣV = V₁ + V₂ +...+ V_i = 0
• ECG example: Leads I, II, and III form a conceptual loop (Einthoven triangle).
  • V_I - V_II + V_III = 0 ⇔ V_I + V_III = V_II

Real batteries and meters

• Electromotive force (EMF): the voltage of a power source (e.g., a battery) when no current is flowing; it represents the ideal maximum voltage the source can provide
• Terminal voltage: the actual voltage across a battery’s terminals, lowered from its EMF by internal resistance when current flows
  • Formula: V_terminal = EMF - I × R_internal
    • Unit: volt (V)
    • V_terminal = terminal voltage of the battery (voltage across the battery terminals under load, V), EMF = electromotive force (ideal battery voltage, V), I = current flowing through the circuit (A), R_internal = battery's internal resistance (Ω)
  • Concept: I × R_internal represents the voltage lost inside the battery as current flows. The voltage drop depends on the current and the internal resistance. The terminal voltage is always less than the EMF when current flows.

A flashlight dims as its battery drains because the battery’s internal resistance reduces the voltage available at the terminals. The terminal voltage is always lower than the battery’s EMF when current flows, and the size of the drop depends on both the current and the internal resistance. As the battery discharges, less voltage reaches the flashlight, providing less energy and causing it to dim.

Magnetic force on charged particles

While stationary charges create electric fields, moving charges (currents) create magnetic fields. A charged particle moving through an external magnetic field will experience a magnetic force.

• Lorentz force (F): the magnetic force experienced by a moving charge in a magnetic field
  • Formula: F = qvBsin(θ)
  • Unit: newton (N)
  • F = magnetic force (N), q = charge (C), v = velocity of the particle (m/s), B = magnetic field strength (T), θ = angle between velocity vector and the magnetic field vector (rad or °)
• Effect on particle motion
  • Because the force is perpendicular to the velocity, magnetic forces do no work on charged particles.
  • The force causes the charged particle to move in a circular or helical path.
• Direction of force (right-hand rule): used to determine the direction of the force
  • The thumb points in the direction of velocity (v).
  • Fingers point in the direction of the magnetic field (B).
  • The force vector (F) for a positive charge points out of the palm. For a negative charge, the force is in the opposite direction (out of the back of the hand).

The magnetic force is always zero if the charge is stationary (v = 0) or moves parallel to the magnetic field lines (θ = 0° or 180°). The force is maximum when the charge moves perpendicular to the field (θ = 90°).

Types of magnetic materials

Diamagnetic materials

• Characteristics: have no unpaired electrons and are slightly repelled by a magnetic field
• Examples: bismuth, copper, gold

Paramagnetic materials

• Characteristics: contain some unpaired electrons and exhibit weak magnetism when exposed to an external magnetic field
• Examples: aluminum, platinum

Ferromagnetic materials

• Characteristics: contain some unpaired electrons and exhibit strong magnetism when exposed to an external magnetic field
• Examples: iron, cobalt, nickel

Induction and inductance

Every electric current generates a magnetic field, which is oriented perpendicular to the direction of current flow. This field can be represented by magnetic field lines, similar to an electric field. Conversely, a changing magnetic field can induce a voltage in a nearby conductor. This phenomenon is called electromagnetic induction.

• Magnetic flux (Φ): a measure of the total number of magnetic field lines passing through a given area
  • Unit: weber (Wb)
• Magnetic flux density (magnetic field strength or B-field): the magnetic flux per unit area, indicating the density or strength of the magnetic field lines
  • Formulas
    • General formula: B = Φ/A
      • Unit: tesla (T) , which is one V⋅s/m² or one Wb/m²
      • B = magnetic flux density (T), Φ = magnetic flux (Wb), A = area (m²)
    • Magnetic field around a straight current-carrying wire: B = (μ₀ × I)/(2π × r)
      • B = magnetic flux density (T), μ₀ = permeability of free space (≈ 4π × 10^-7 T⋅m/A), I = current (A), r = distance from the wire (m)
    • Magnetic field at the center of a circular loop of wire carrying current: B = (μ₀ × I)/(2 × R)
      • B = magnetic flux density (T), μ₀ = permeability of free space (≈ 4π × 10^-7 T⋅m/A), I = current (A), R = radius of the loop (m)
• Inductance (L): a property of an electrical component (e.g., a coil) that describes its ability to induce a voltage in itself (self-induction) or in a nearby component in response to a change in current
  • Inductance is the ratio of the induced voltage to the rate of change of the current.
    • Formula: V = -L × (dI/dt)
      • Unit: henry (H)
      • V = induced voltage (V), L = inductance (H), dI/dt = rate of change of current (A/s)

Devices such as pacemakers utilize inductance principles to regulate heart rhythms. In MRI technology, inductance is crucial for generating the strong magnetic fields necessary for imaging.

Magnetic flux density describes the strength of a magnetic field, while inductance is a property of an electrical component, such as a coil.

Transformer

A transformer is a component that uses electromagnetic induction to increase (step-up) or decrease (step-down) AC voltage.

• Consists of a primary coil and a secondary coil
• An alternating current in the primary coil generates a changing magnetic field, which induces an alternating current in the secondary coil, even without physical connection.
• Ideal transformer equation: V₂/V₁ = n₂/n₁
  • V = voltage (V), n = number of turns in the coil; subscript 1 refers to the primary coil and 2 to the secondary coil (unitless)