Electrical Properties: Charge, Electrostatics, Potential, and Conductors

Electrical Properties in Physics

Learning Objectives

• Understand the nature of charge (positive & negative) and the interactions between charges.

• Describe electric current (I; Amps) as the rate of flow of charge (Q; Coulombs).

• Understand the meaning of voltage (V; volts) and its significance as energy per unit charge.

• Apply the concept that resistance is defined as $R = \frac{V}{I}$ and use Ohm's Law ($V = IR$).

• Recognize conductance (G; siemens) as the reciprocal of resistance.

• Recall and use expressions for combinations of resistors or conductors in series and parallel.

• Recognize and use the relationships between I, V, and R to analyze simple series and parallel electrical circuits.

• Appreciate that capacitors (C; farads) store charge and relate Q, C, and V.

• Understand that capacitors charge and discharge in an exponential manner.

Ions and Charge

Definition and Types of Ions

Ions are atoms or molecules with a net electric charge due to an unequal number of electrons (-ve) and protons (+ve) in their structure.

• Cations: Positively charged ions (e.g., Na+) formed by loss of electrons.

• Anions: Negatively charged ions (e.g., Cl-) formed by gain of electrons.

Example: Sodium ion (Na+) loses an electron to achieve a stable electron configuration, becoming a cation. Chloride ion (Cl-) gains an electron, becoming an anion.

Electrostatics

Forces Between Charges

Electrostatics studies the forces between stationary electric charges. Ions of like charge repel each other, while ions of opposite charge attract each other by an electrostatic (Coulombic) force.

• The force ($F$) between two point charges is inversely proportional to the square of the distance ($r$) between them:

$F \propto \frac{1}{r^2}$

• Ionic bonds can be formed between ions of opposite charge due to electrostatic attraction.

Charge

Units and Constants

• The unit of charge is the coulomb (C).

• Symbol used in equations is usually Q (sometimes q).

• The elementary charge ($e$) of an electron is $1.602 \times 10^{-19}$ C.

• The Faraday constant (F) is the charge on 1 mole of electrons:

$F = 9.648 \times 10^4 \text{ C mol}^{-1}$

Example: The charge on 1 mole of electrons is calculated using Avogadro's number and the elementary charge.

The Electrostatic Field

Definition and Mapping

An electric field is a region where an electric force is experienced. It can be mapped by electrostatic lines of force (also called electric flux).

• By convention, the direction of the field is the direction of the force on a small positive charge.

• Lines of force radiate outward from positive charges and inward toward negative charges.

Force in an Electric Field

• The force ($F$) on a charged body within an electric field depends on:

  • The charge on the body ($Q$)

  • The strength of the field ($E$; units: N/C)

$F = EQ$

Example: For a small test charge $Q'$ in a field $E$, the force experienced is $F = EQ'$.

The Concept of Potential

Gravitational and Electrical Potential

Potential energy is the energy stored due to an object's position in a field. In gravity, it depends on height above the earth; in electricity, it depends on position in the electric field.

• Points closer to the source of the field have higher potential.

• Equipotentials are surfaces where the potential is constant.

The Unit of Potential: The Volt (V)

Definition and Measurement

Electrical potential (V) is similar to gravitational potential. It is measured in volts (V), where 1 volt is 1 joule per coulomb.

$1\ \text{V} = 1\ \text{J}\ \text{C}^{-1}$

• Potential difference increases with proximity to the charge.

• Work ($W$) required to move a charge ($Q$) through a potential difference ($V$):

$W = QV$

Example: Moving a charge from point A to B in an electric field requires work equal to the product of charge and potential difference.

Electrostatics, Work and Energy

Energy in Charge Interactions

• Repulsion between like charges requires energy input (work done).

• Attraction between opposite charges releases energy.

Example: In biological molecules, positively charged side chains (e.g., arginine) repel cations, while negatively charged side chains (e.g., aspartate) attract cations.

Electrostatics in Action in Biology

Movement of Ions Across Membranes

Biological membranes are selectively permeable to ions. Ion channels facilitate rapid movement of ions, often with selectivity for cations (e.g., Na+) or anions (e.g., Cl-).

• Phospholipid bilayer is impermeant to ions without protein channels.

• Channels can be selective for specific ions, affecting cellular charge distribution.

Charge Distribution and Potential Difference

Asymmetric Distribution

• Regions with high concentration of positive ions have high positive potential.

• Regions with more negative ions have negative potential.

• Potential difference arises from asymmetric charge distribution.

Voltages in Biology

Measurement and Units

• Potential difference is the energy expended or released when moving a charge between two points in an electric field.

• Measured in volts (V); in biology, millivolts (mV) are often used ($1\ \text{V} = 1000\ \text{mV}$).

• Membrane potential ($V_m$) can be measured using microelectrodes and voltmeters.

Example: The membrane potential is the difference in potential between the inside and outside of a cell.

Conductors

Definition and Mechanisms

• Conductors are materials that transmit charge.

• In metals, conduction is by free electrons; in biology, by ions in electrolyte solutions.

• Free electrons in metals move randomly without a field; with an electric field, they drift in the direction of the field.

Conductors in Biology

• Positively charged ions move toward negative potential (cathode).

• Negatively charged ions move toward positive potential (anode).

Electrolytes and Non-Electrolytes

• Electrolytes: Compounds whose aqueous solutions conduct electricity (e.g., salts).

• Non-electrolytes: Compounds that dissolve in water but do not conduct electricity (e.g., many non-metals).

Appendix: Important Terms and Units

Abbreviation	Physical Property	Unit	Unit Symbol
Q, q	charge	coulomb	C
I, i	current	ampere	A
V	electrical potential (potential difference)	volt	V
R, r	resistance	ohm	Ω
G	conductance	siemens	S
ρ (rho)	resistivity	ohm·metre	Ω·m
Cc	capacitance	farad	F

Additional info: These notes expand on the original slides by providing full definitions, equations in LaTeX, and examples relevant to both physics and biological contexts. The table above summarizes key physical quantities and their units for reference.