physics (1)

Chapter 23: Biological Applications of Electric Fields and Potentials

23.1 Capacitance and Capacitors

• Introduction to Electric Fields and Potentials

  • Explores practical devices and physiological processes using electric fields and potentials.

  • Focus on capacitors to store charge and energy, leading to discussions about cell membranes and ions.

• Capacitance and Charge Separation

  • Potential difference arises from charge separation (e.g., transferring charge Q between conductors).

  • Opposite charges form a capacitor: +Q on one conductor and -Q on the other.

• Properties of Capacitors

  • Electric field strength (E) and potential difference (∆VC) increase with charge on the electrodes.

  • Relationship:

    • Q = C * ∆VC (23.1)

  • Capacitance (C)

    • Depends on electrode shape, size, and separation.

    • SI Unit: farad (F), with practical capacitors ranging from picofarads (pF) to microfarads (µF).

• Charging a Capacitor

  • Charging involves moving charge from one electrode to another via a battery.

  • Current continues until capacitor voltage matches battery voltage.

  • Once disconnected, the capacitor retains its charge.

23.2 The Parallel-Plate Capacitor

• Design and Electric Field

  • Parallel-plate capacitors produce a uniform electric field:

    • E = Q / (ε0A) (23.2)

  • Capacitance relationship:

    • C = (ε0 * A) / d (23.3)

      • A = area, d = separation distance.

• Example Calculations

  • Example of calculating charge based on capacitance and potential difference.

• Energy Stored in a Capacitor

  • Charge (q) establishes a potential difference (∆V), resulting in stored energy:

    • UC = (1/2 * Q * ∆V) = (Q² / (2C)) (23.5)

    • Energy density:

      • uE = (1/2 * ε0 * E²) (23.8)

• Rapid Energy Release

  • Capacitors can store charge and release energy quickly (e.g., camera flash, defibrillator).

    • Comparison to mechanical systems like catapults for understanding energy release.

23.3 Dielectrics

• Dielectrics

  • Introduction of a dielectric material between capacitor plates increases capacitance:

    • C = k * C0 (23.18), where k = dielectric constant.

  • Impact on electric fields due to polarization from dielectric materials.

• Point Charge in a Dielectric

  • Electric field and potential reduction factors include dielectric constant effects.

• Debye Length

  • Affected by ion concentration and thermal energy, crucial for understanding the ionic environment in solutions (e.g., saltwater).

23.4 Electrostatics in Salt Water

• Charged Electrode Dynamics

  • Opposition forces from ions surround charged electrodes in salt water.

  • Electric fields decrease with distance, denoted by the Debye length (lD).

    • lD = sqrt((ε * kB * T)/(e²c0)) (23.24), defining ion behavior and concentration gradients.

23.5 The Membrane Potential of a Cell

• Membrane and Ions

  • Establishing a membrane potential with concentration gradients of K+ and Na+ ions.

    • Key phenomenon: outward flow of K+ balanced by inward electric field.

    • Model of cell membrane as a capacitor, leading to concepts of Nernst potential:

      • VK_Nernst = (RT/zF) * ln(c_out/c_in) (23.30).

• Sodium-Potassium Pumps

  • Role in maintaining steady-state concentrations of ions within cells.

Summary

• Key Points to Remember

  • Electric fields play crucial roles in various biological systems.

  • Capacitors and their properties relate directly to physiological processes and cell functions.

  • Understanding the calculations for charge, capacitance, energy, and the effects of dielectrics is essential in the context of electric fields and their applications in biology.