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∣q<em>1q</em>2∣r2F = k \frac{|q<em>1 q</em>2|}{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=Fq0E = \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=kqr2E = 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=ΔU=U(B)−U(A)W = \Delta U = U(B) - U(A)

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

    • Potential Energy:

    • Expressed as:

      • U=kq<em>1q</em>2rU = k \frac{q<em>1 q</em>2}{r}

    • Energy measured in Joules (J).

Electric Potential

  • Electric Potential ($V$) Definition:

    • Change in electric potential energy per charge:

    • V=UqV = \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:

    • ΔU=∫E⋅dr\Delta U = \int E \cdot dr

    • In uniform electric fields, simplifies to:

      • ΔU=E⋅d\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=QVC = \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=qEF = ma = qE

  • Viscous forces:

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

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

    • Vd=qEηV_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=QtI = \frac{Q}{t}

    • Measured in Amperes (A).

  • Voltage and Ohm’s Law:

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

    • I=VRI = \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:

    • R<em>t=R</em>1+R<em>2+…+R</em>nR<em>t = R</em>1 + R<em>2 + … + R</em>n

  • Resistors in Parallel:

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

    • 1R<em>t=1R</em>1+1R<em>2+…+1R</em>n\frac{1}{R<em>t} = \frac{1}{R</em>1} + \frac{1}{R<em>2} + … + \frac{1}{R</em>n}

Power Dissipation in Resistors

  • Power as Energy per Time:

    • Expressed as:

    • P=ΔUtP = \frac{\Delta U}{t}

    • Related to ohm's law as:

      • P=I2RP = I^2 R

      • P=V2RP = \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.