Summary of Charges, Forces, Electric Fields, and Circuits in Physics

Introduction to Physical Quantities in Atomic Scale

• Overview of various physical quantities crucial for understanding atomic interactions.

Atomic Structure

• Charges: Key components of atomic structures are charges.

  • Anatomy of an atom:

  • Nucleus: Contains protons and neutrons.

  • Electrons: Revolve around the nucleus and engage in chemical bonding.

  • Behavior of electrons:

  • Only electrons can move and share between atoms.

  • Influences electrical conductivity in materials (particularly conductors).

Fundamental Forces

• Coulomb Force:

  • Definition: The force between two charges given by the formula:

  • F = k \frac{|q1 q2|}{r^2}

  • Characteristics:

  • Varies with the product of the interacting charges.

  • Inversely proportional to the square of the distance between charges.

  • Can be attractive (opposite charges) or repulsive (like charges).

  • Force as pairs: Considered as action-reaction pairs, analogous to gravitational forces.

Electric Field

• Electric Field Definition:

  • Electric field ($E$) around a charge, defined as:

  • E = \frac{F}{q_0}

  • Where $F$ is the force acting on a test charge $q_0$.

  • Interaction of charges with a probe charge:

  • Represented by its effect on a test charge placed in the field.

  • Formulating electric field, relating to distance and charge:

  • E = k \frac{q}{r^2} at a distance $r$ from charge $q$.

Electrostatic Work and Energy

• Work Definition:

  • Work (W) done by electrostatic force moving a charge from point A to B:

  • W = \Delta U = U(B) - U(A)

  • Where potential energy ($U$) relates to the configuration of charges.

  • Potential Energy:

  • Expressed as:

    • U = k \frac{q1 q2}{r}

  • Energy measured in Joules (J).

Electric Potential

• Electric Potential ($V$) Definition:

  • Change in electric potential energy per charge:

  • V = \frac{U}{q}

  • Units: Measured in Volts (V).

  • Equipotential surfaces: Points equidistant from the charge exhibit the same potential.

  • Defined mathematically using distance from charge.

  • Relationship between electric field and potential:

  • \Delta U = \int E \cdot dr

  • In uniform electric fields, simplifies to:

    • \Delta U = E \cdot d for small displacements.

Capacitors

• Capacitor Structure:

  • Contains two conductive plates with separation distance, one charged positively and the other negatively.

  • Electric field is perpendicular between the plates.

  • Dielectric material: Affects capacitance ($C$) defined by:

  • C = \frac{Q}{V}

  • Capacitance Influences: Related to area of plates and distance between them, as well as dielectric constant.

Charge Movement in Electric Fields

• Charge behavior in Electric Fields:

  • When positive charge moved within an electric field, it experiences acceleration due to electrostatic forces.

  • Newton's second law applied results in the force:

  • F = ma = qE

• Viscous forces:

  • In cases where movement occurs in a viscous medium, additional forces oppose motion.

  • Drift velocity ($V_d$) is defined as:

  • V_d = \frac{qE}{\eta}

  • Where $ an{IEEE}$ indicates the viscous coefficient characterizing the medium.

  • Applications: Important in biological contexts like gel electrophoresis.

Current in Conductors

• Definition of Electric Current ($I$):

  • Rate of charge flow per unit time.

  • I = \frac{Q}{t}

  • Measured in Amperes (A).

• Voltage and Ohm’s Law:

  • Relation among current, voltage ($V$), and resistance ($R$):

  • I = \frac{V}{R}

  • Resistance is measured in Ohms (Ω).

Kirchhoff's Laws

• First Law (Junction Rule):

  • The sum of currents entering and exiting a junction equals zero.

• Second Law (Loop Rule):

  • The sum of potential differences around a closed circuit loop equals zero.

Series and Parallel Resistors

• Resistors in Series:

  • Total resistance ($R_t$) is the sum of individual resistances:

  • Rt = R1 + R2 + … + Rn

• Resistors in Parallel:

  • Total resistance is given by the inverse sum of the resistances:

  • \frac{1}{Rt} = \frac{1}{R1} + \frac{1}{R2} + … + \frac{1}{Rn}

Power Dissipation in Resistors

• Power as Energy per Time:

  • Expressed as:

  • P = \frac{\Delta U}{t}

  • Related to ohm's law as:

    • P = I^2 R

    • P = \frac{V^2}{R}

Biological Applications of Electric Circuits

• Cellular Membrane as Circuit:

  • Acts as a capacitor separating extracellular and intracellular spaces.

  • Differential ion concentrations create a voltage across the membrane (typically around 90 mV).

• Ionic Pumps:

  • Regulate ion concentrations to maintain membrane potential, ensuring essential cellular functions remain active.

• Capacitor analogy:

  • The cellular membrane's capacity to maintain potential mimics that of capacitors in electrical circuits.