Electric Charge and Coulomb's Law

• Electricity involves the flow of electric charge, a fundamental property of matter.
• Electric charge is quantized; it exists in discrete units.
• The elementary charge, denoted as 'e', is the smallest unit of charge found in nature.
• Protons have a positive charge (+e), and electrons have a negative charge (-e).
• Neutrons are neutral, possessing no electric charge.
• Like charges repel each other, while opposite charges attract.

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.
• The force is inversely proportional to the square of the distance between the charges.
• Mathematically, Coulomb's Law is expressed as: F = k * (|q1 * q2|) / r², where:
  • F is the electrostatic force.
  • k is Coulomb's constant (approximately 8.99 x 10^9 N⋅m²/C²).
  • q1 and q2 are the magnitudes of the charges.
  • r is the distance between the charges.
• The force is a vector quantity, having both magnitude and direction.
• The direction of the force is along the line joining the two charges.
• The force is repulsive if the charges have the same sign and attractive if they have opposite signs.

Electric Field

• An electric field is a region of space around a charge where another charge would experience a force.
• Electric field strength (E) is defined as the force per unit positive charge.
• E = F/q, where:
  • E is the electric field strength (N/C or V/m).
  • F is the electric force (N).
  • q is the test charge (C).
• Electric fields are vector quantities, with both magnitude and direction.
• The direction of the electric field is the direction of the force on a positive test charge.
• Electric field lines are used to visualize electric fields:
  • They originate from positive charges and terminate on negative charges.
  • The density of the lines indicates the strength of the field.
  • Electric field lines never cross each other.
• The electric field due to a point charge q at a distance r is given by: E = k * |q| / r².
• Superposition principle applies to electric fields: the total electric field at a point due to multiple charges is the vector sum of the electric fields due to each individual charge.

Conductors and Insulators

• Conductors are materials that allow electric charge to move freely through them.
• Metals, such as copper and aluminum, are good conductors due to the presence of free electrons.
• In conductors, electric fields are zero inside the material in electrostatic equilibrium.
• Excess charge on a conductor resides on its surface.
• Insulators (also called dielectrics) are materials that do not allow electric charge to move freely.
• Examples of insulators include glass, rubber, and plastic.
• In insulators, electrons are tightly bound to atoms and cannot move easily.
• When an insulator is placed in an electric field, it becomes polarized.

Electric Force

• The electric force is a fundamental force of nature that acts between charged objects.
• It is responsible for many phenomena, including chemical bonding, the behavior of electronic devices, and atmospheric phenomena like lightning.
• The electric force is much stronger than the gravitational force.
• The electric force is a conservative force, meaning the work done by the electric force is independent of the path taken.
• The electric potential energy (U) of a charge q at a point in an electric field is the potential energy it has due to its position in the field.
• The change in electric potential energy (ΔU) is equal to the negative of the work done by the electric force: ΔU = -W.
• Electric potential (V) is the electric potential energy per unit charge: V = U/q.
• The unit of electric potential is the volt (V), where 1 V = 1 J/C.
• Potential difference (ΔV) between two points is the work done per unit charge to move a charge from one point to another.

Capacitors

• A capacitor is a device that stores electrical energy in an electric field.
• It consists of two conductors (plates) separated by an insulator (dielectric).
• When a voltage is applied across the capacitor, charges accumulate on the plates.
• One plate accumulates positive charge, and the other accumulates negative charge.
• The capacitance (C) of a capacitor is a measure of its ability to store charge.
• C = Q/V, where:
  • C is the capacitance (Farads, F).
  • Q is the charge stored on the capacitor (Coulombs, C).
  • V is the voltage across the capacitor (Volts, V).
• The capacitance of a parallel-plate capacitor is given by: C = ε₀ * (A/d), where:
  • ε₀ is the permittivity of free space (approximately 8.85 x 10^-12 F/m).
  • A is the area of each plate.
  • d is the distance between the plates.
• The energy stored (U) in a capacitor is given by: U = (1/2) * C * V² = (1/2) * Q² / C = (1/2) * Q * V
• Capacitors can be connected in series or parallel.
• For capacitors in series:
  • The reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances: 1/Ceq = 1/C1 + 1/C2 + ...
  • The charge is the same on each capacitor.
  • The voltage across the series combination is the sum of the voltages across each capacitor.
• For capacitors in parallel:
  • The equivalent capacitance is the sum of the individual capacitances: Ceq = C1 + C2 + ...
  • The voltage is the same across each capacitor.
  • The total charge on the parallel combination is the sum of the charges on each capacitor.
• Dielectrics increase the capacitance of a capacitor and allow it to store more energy.
• When a dielectric material is inserted between the plates of a capacitor, the capacitance increases by a factor of κ (the dielectric constant).
• C' = κ * C, where C' is the new capacitance with the dielectric, and C is the original capacitance.