Electric Charges and Fields: Coulomb's Law and Electric Potential

Electric Charges and Fields

Coulomb's Law

• Describes the electric force between two point charges
• Mathematically represented as: F = k * (q1 * q2) / r^2
  • F: electric force between the charges
  • k: Coulomb's constant (8.99 x 10^9 N m^2 C^2)
  • q1 and q2: magnitudes of the two point charges
  • r: distance between the centers of the charges
• Electric force is repulsive if charges have the same sign, attractive if they have opposite signs

Electric Potential

• Electric potential (V) at a point in space is the potential energy per unit charge
• Measured in volts (V)
• Electric potential due to a point charge: V = k * q / r
  • V: electric potential
  • k: Coulomb's constant
  • q: magnitude of the point charge
  • r: distance from the point charge
• Electric potential is a scalar quantity

Charge Distribution

• Types of charge distributions:
  • Point charge: localized charge
  • Line charge: charge distributed along a line
  • Surface charge: charge distributed over a surface
  • Volume charge: charge distributed throughout a volume
• Charge density (λ, σ, or ρ) describes the amount of charge per unit length, area, or volume

Electric Field Lines

• Electric field lines (E-field lines) are imaginary lines that emerge from positive charges and enter negative charges
• Properties of E-field lines:
  • They are continuous and unbroken
  • They emerge from positive charges and enter negative charges
  • They never intersect
  • They are tangent to the electric field at every point
• Electric field lines can be used to visualize the electric field around a charge or system of charges

Gauss's Law

• Relates the distribution of electric charge to the resulting electric field
• Mathematically represented as: ∫E · dA = Q / ε₀
  • E: electric field
  • dA: area element of the Gaussian surface
  • Q: total charge enclosed within the Gaussian surface
  • ε₀: electric constant (permittivity of free space)
• Gauss's law can be used to calculate the electric field due to a symmetric charge distribution

Electric Charges and Fields

Coulomb's Law

• Electric force between two point charges is described by Coulomb's Law
• The law is mathematically represented as F = k * (q1 * q2) / r^2
• Electric force is repulsive if charges have the same sign, attractive if they have opposite signs
• Coulomb's constant (k) is 8.99 x 10^9 N m^2 C^2

Electric Potential

• Electric potential (V) is the potential energy per unit charge
• It is measured in volts (V)
• Electric potential due to a point charge is V = k * q / r
• Electric potential is a scalar quantity

Charge Distribution

• There are four types of charge distributions: point charge, line charge, surface charge, and volume charge
• Charge density (λ, σ, or ρ) describes the amount of charge per unit length, area, or volume

Electric Field Lines

• Electric field lines (E-field lines) are imaginary lines that emerge from positive charges and enter negative charges
• E-field lines are continuous and unbroken
• They emerge from positive charges and enter negative charges
• They never intersect
• They are tangent to the electric field at every point

Gauss's Law

• Gauss's Law relates the distribution of electric charge to the resulting electric field
• The law is mathematically represented as ∫E · dA = Q / ε₀
• Electric constant (ε₀) is the permittivity of free space
• Gauss's law can be used to calculate the electric field due to a symmetric charge distribution