Electric Charge and Coulomb's Law

Millikan's Oil Drop Experiment

• Demonstrated the quantized nature of electric charge.
• Established that charge exists in whole multiples of elementary charge (e), prohibiting fractional charges.

Conservation of Charge

• The total charge in an isolated system is constant over time.
• Charge can only be transferred, not created or destroyed.

Electric Charge Properties

• Electric charge is additive, determined by the algebraic sum of individual charges.
• Charge remains invariant, independent of motion or observation.

Coulomb's Law

• Describes the electrostatic force between two point charges: $$F = \frac{1}{4\pi\epsilon_0} \frac{q_1q_2}{r^2}$$
• $F$ is the force between charges $q_1$ and $q_2$, separated by distance r.
• $\epsilon_0$ (permittivity of free space) is approximately $8.85 \times 10^{-12} \text{ C}^2/\text{N m}^2$ or $9 \times 10^{9} \text{ Nm}^2/\text{C}^2$ in inverse form.
• In a medium, $\epsilon_0$ changes to $\epsilon_0 \epsilon_r$ (dielectric constant).

Continuous Charge Distribution Types

• Charge can distribute continuously in three ways:
  • Linear Charge Distribution
  • Surface Charge Distribution
  • Volume Charge Distribution

Linear Charge Distribution

• Linearly distributed charge expressed as: $$dq = \lambda dl$$
• Forces calculated via: $$dF = \frac{1}{4\pi\epsilon_0} \frac{q_0\lambda dl}{r^2}$$
• Net force on charge $q_0$: $$F = \frac{q_0\lambda}{4\pi\epsilon_0} \int \frac{dl}{r^2}$$

Surface Charge Distribution

• Surface charge density expressed as: $$dq = \sigma dS$$
• Total force on charge $q_0$: $$F = \frac{q_0}{4\pi\epsilon_0} \int \frac{\sigma dS}{r^2}$$

Volume Charge Distribution

• Volume charge density represented as: $$dq = \rho dV$$

Electric Field Intensity

• Defined as electric force per unit positive charge: $$E = \lim_{q_0 \to 0} \frac{F}{q_0}$$
• SI units are N/C or V/m; it's a vector quantity.

Electric Field Intensity Due to a Point Charge

• Given by: $$E = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2}$$
• For a positive charge, field lines point radially outward; for a negative charge, they point inward.

Electric Dipole in Uniform Electric Field

• Dipole orientation impacts stability; parallel alignment is stable, while antiparallel is unstable.

Gauss's Law

• Relates electric flux through a closed surface to the enclosed charge: $$\oint \vec{E} \cdot \vec{dA} = \frac{q}{\epsilon_{0}}$$
• Specific Gaussian surface shapes depend on charge configurations (spherical, cylindrical, etc.).

Electric Field Due to Specific Charge Distributions

• Thin, infinitely long straight wire: $$E = \frac{\lambda}{2\pi\epsilon_{0}r}$$
• Uniformly charged thin spherical shell:
  • Outside shell ($r>R$): $$E = \frac{1}{4\pi\epsilon_0}\frac{q}{r^{2}}$$
  • On the shell ($r=R$): $$E = \frac{1}{4\pi\epsilon_0}\frac{q}{R^{2}}$$
  • Inside shell ($r<R$): Field intensity is zero.

This quiz covers key concepts in electrostatics, including Millikan's oil drop experiment, the conservation of charge, and the properties of electric charge. It also explains Coulomb's Law and how it quantifies the electrostatic force between point charges. Test your understanding of these fundamental principles of physics.