Electric Charge and Electric Field: Physics for Bioscience and Bioengineering

Electric Charge and Electric Field

Introduction to Electric Charge

Electric charge is a fundamental property of matter that gives rise to electric forces and fields. The study of electric charge is essential in understanding many biological and engineering phenomena, especially those involving ions, molecules, and cellular processes.

• Unit of Charge: The SI unit of electric charge is the coulomb (C).

• Quantization: Electric charge is quantized in units of the elementary charge, e.

• Elementary Charge: The charge of an electron is $q_{elect.} = -e$, where $e = 1.602 imes 10^{-19}$ C.

• Historical Note: The unit is named after Charles-Augustin de Coulomb, a French engineer and physicist.

Charge in the Atom

Atoms consist of protons, neutrons, and electrons, each with distinct properties and charges.

• Proton: Mass $m_p = 1.67 imes 10^{-27}$ kg, charge $q = +e$.

• Electron: Mass $m_e = 9.11 imes 10^{-31}$ kg, charge $q = -e$.

• Neutron: Electrically neutral, mass about 2000 times heavier than the electron ($m_n = 1836 m_e$).

• Neutral Atom: Number of electrons equals number of protons, resulting in zero net charge.

• Example: A neutral lithium atom has 3 protons, 4 neutrons, and 3 electrons.

Conductors and Insulators

Materials are classified based on how freely their electrons can move, which affects their electrical properties.

• Insulators: Electrons are tightly bound to nuclei and cannot move freely. Charging by friction leaves localized patches of charge.

• Conductors: Outer (valence) electrons are only weakly bound and can move throughout the material, forming a 'sea of electrons'.

• Metals: Good conductors due to mobile valence electrons.

Estimating Number of Electrons in Water

Understanding the number of electrons in biological substances is important for bioengineering applications.

• Molar Mass of Water: Approximately 18 g/mol.

• Density of Water: $\rho = 1000 \frac{kg}{m^3}$.

• Avogadro's Number: $6 \times 10^{23}$ molecules/mol.

• Calculation Example:

  • 1 L of water has mass 1 kg.

  • Number of moles: $n = \frac{1.0 \text{ kg}}{0.018 \text{ kg/mol}} \approx 55.6$ mol.

  • Number of molecules: $N = 55.6 \times 6 \times 10^{23} \approx 3.3 \times 10^{25}$ molecules.

  • Each H2O molecule has 10 electrons (2 from H, 8 from O).

  • Total electrons: $N_e = 3.3 \times 10^{25} \times 10 = 3.3 \times 10^{26}$ electrons.

Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a distance. Dipoles are common in molecules such as water, which is crucial in biological systems.

• Definition: A pair of point charges of equal magnitude but opposite sign, separated by a distance.

• Example: The water molecule (H2O) forms an electric dipole due to its molecular geometry and charge distribution.

• Dipole Moment: The dipole moment vector points from the negative to the positive charge.

• Applications: Dipoles play a key role in molecular interactions, solubility, and the behavior of substances in electric fields.

Table: Comparison of Conductors and Insulators

Property	Conductors	Insulators
Electron Mobility	High (valence electrons move freely)	Low (electrons tightly bound)
Charge Distribution	Uniform, can move throughout material	Localized, remains in patches
Examples	Metals (Cu, Ag)	Glass, rubber

Table: Atomic Particles

Particle	Charge	Mass (kg)
Proton	+e	1.67 × 10-27
Electron	-e	9.11 × 10-31
Neutron	0	1.67 × 10-27

Key Equations

• Elementary Charge: $e = 1.602 \times 10^{-19}$ C

• Number of Molecules: $N = n \times N_A$

• Number of Electrons in Water: $N_e = N \times 10$

Summary

• Electric charge is a quantized property carried by protons and electrons.

• Atoms are electrically neutral when the number of protons equals the number of electrons.

• Conductors allow free movement of electrons, while insulators do not.

• Dipoles are important in molecular physics and bioengineering.

• Estimating electron numbers in substances is useful for understanding electrical properties in biological contexts.

Additional info: Some calculations and context have been expanded for clarity and completeness.