Electrostatics: Electric Charge and Coulomb's Law

• Electrostatics is the study of stationary electric charges and the forces between them.

Electric Charge

• Electric charge is a fundamental property of matter carried by elementary particles.
• The most common carrier of negative charge is the electron.
• The most common carrier of positive charge is the proton.
• Charge is quantized, meaning it exists in discrete units.
• The elementary unit of charge is denoted as 'e', approximately equal to 1.602 x 10^-19 Coulombs.
• Objects can be charged through various methods, including friction (triboelectric effect), conduction, and induction.
• Like charges repel each other, and opposite charges attract each other.
• Charge is conserved in a closed system, meaning the total amount of charge remains constant.

Coulomb's Law

• Coulomb's Law quantifies the electrostatic force between two point charges.
• The force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
• Mathematically, Coulomb's Law is expressed as: F = k * (|q1 * q2|) / r^2, where:
  • F is the electrostatic force
  • k is Coulomb's constant (approximately 8.9875 x 10^9 N m^2/C^2)
  • q1 and q2 are the magnitudes of the charges
  • r is the distance between the charges
• The force is attractive if the charges have opposite signs and repulsive if they have the same sign.
• Coulomb's Law is a vector equation; the force acts along the line connecting the two charges.

Electric Field

• An electric field is a region of space around a charged object in which another charged object experiences a force.
• The electric field intensity (E) is defined as the force per unit positive charge: E = F/q, where:
  • E is the electric field intensity (N/C or V/m)
  • F is the electrostatic force (N)
  • q is the test charge (C)
• Electric field lines are used to visualize electric fields; they point in the direction of the force on a positive test charge.
• Electric field lines originate from positive charges and terminate on negative charges.
• The density of electric field lines indicates the strength of the electric field.
• The electric field due to a point charge q at a distance r is given by: E = k * q / r^2.

Electric Potential

• Electric potential (V) is the amount of work needed to move a unit positive charge from a reference point to a specific point inside an electric field.
• Electric potential is measured in volts (V).
• The potential difference between two points A and B is the work done in moving a unit positive charge from A to B: V_B - V_A = W/q.
• The electric potential due to a point charge q at a distance r is given by: V = k * q / r.
• Equipotential surfaces are surfaces where the electric potential is constant.
• Electric field lines are always perpendicular to equipotential surfaces.

Conductors, Insulators, and Semiconductors

• Conductors are materials that allow electric charge to move freely through them (e.g., metals).
• In conductors, electrons are loosely bound and can easily move under the influence of an electric field.
• Insulators are materials that do not allow electric charge to move freely through them (e.g., rubber, glass).
• In insulators, electrons are tightly bound and require a large amount of energy to move.
• Semiconductors have conductivity between that of conductors and insulators (e.g., silicon, germanium).
• The conductivity of semiconductors can be controlled by adding impurities (doping).

Electric Potential Energy

• Electric potential energy (U) is the energy a charge possesses due to its position in an electric field.
• The change in electric potential energy when a charge q is moved between two points A and B is given by: ΔU = q * (V_B - V_A).
• The electric potential energy of a system of two point charges q1 and q2 separated by a distance r is given by: U = k * (q1 * q2) / r.
• If the charges have the same sign, the potential energy is positive (repulsive force).
• If the charges have opposite signs, the potential energy is negative (attractive force).

Capacitance and Capacitors

• Capacitance (C) is a measure of a capacitor's ability to store electric charge.
• A capacitor is a device consisting of two conductors separated by an insulator (dielectric).
• Capacitance is defined as the ratio of charge (Q) stored on the capacitor to the potential difference (V) across it: C = Q/V.
• The unit of capacitance is the farad (F).
• For a parallel-plate capacitor, the capacitance is given by: C = ε_0 * (A/d), where:
  • ε_0 is the permittivity of free space (approximately 8.854 x 10^-12 F/m)
  • A is the area of each plate
  • d is the separation between the plates
• The energy stored in a capacitor is given by: U = (1/2) * C * V^2 = (1/2) * Q * V = (1/2) * (Q^2 / C).

Dielectrics

• A dielectric is an insulating material placed between the plates of a capacitor to increase its capacitance.
• The dielectric constant (κ) is the factor by which the capacitance increases when a dielectric is inserted: C' = κ * C.
• Inserting a dielectric reduces the electric field strength between the plates of the capacitor.
• Dielectrics have a breakdown voltage, above which they become conductive.

Applications of Electrostatics

• Electrostatics has numerous applications in various fields, including:
  • Xerography (photocopiers and laser printers)
  • Electrostatic painting and coating
  • Air pollution control (electrostatic precipitators)
  • Medical applications (e.g., electrostatic drug delivery)
  • Electronic devices (e.g., capacitors in circuits)