Electric Field Intensity and Point Charge Dynamics

Fundamentals of Electric Charges and Electric Fields

  • Charge is a scalar physical quantity.
  • An electric field exists in the region surrounding an electric charge, such as a point charge +Q+Q or −Q-Q located at an origin point OO.
  • Electric fields exert electrostatic forces on other charged particles introduced into the surrounding space.

Electric Field Patterns

  • Electric field patterns provide a visual representation of the directional lines of force surrounding charged objects.
  • Key field patterns include:
    • Electric field pattern around a positive charge: Field lines extend radially outward in all directions away from a isolated positive point charge +Q+Q.
    • Electric field pattern between two unlike point charges: Field lines originate on the positive point charge +Q+Q and terminate on the negative point charge −Q-Q, illustrating mutual electrostatic attraction.
  • Reference figures:
    • Fig. 1.5: Electric field pattern illustrating:
    • (a) Electric field pattern around a positive charge.
    • (b) Electric field pattern between two unlike point charges.
    • Fig. 1.6: Electric field EE due to a positive point charge +Q+Q.
    • Fig. 1.7: Electric field EE due to a negative point charge −Q-Q.

Electric Field Intensity (EE)

  • Definition: Electric field intensity EE (also termed electric field strength) at a given point is defined as the force per unit positive test charge placed at that point.
  • Vector Nature: Electric field intensity EE is a vector quantity.
  • Direction of EE: The direction of the electric field intensity vector EE at any point corresponds directly to the direction of the force exerted on a positive test charge placed at that point:
    • Points radially away from a positive source charge +Q+Q.
    • Points radially toward a negative source charge −Q-Q.
  • Units of Measurement:
    • Newton per coulomb, written as N C−1\text{N C}^{-1} or N/C\text{N/C}.
    • Volt per metre, written as V m−1\text{V m}^{-1} or V/m\text{V/m}.

Electric Field Intensity Due to a Point Charge

  • Theoretical Framework:
    • Consider a source point charge +Q+Q located at origin point OO, creating an electric field in the surrounding space.
    • To determine the electric field intensity EE at point PP, located at a radial distance rr from point OO, a positive test charge +q+q is placed at point PP.
  • Electrostatic Force via Coulomb's Law:
    • According to Coulomb's law, the electrostatic force FF acting on the test charge +q+q at point PP due to charge QQ at point OO is:     F=14πε0Qqr2F = \frac{1}{4\pi\varepsilon_0} \frac{Q q}{r^2}
  • Mathematical Expression for Electric Field Intensity:
    • The magnitude of the electric field intensity EE is defined as the electrostatic force per unit test charge:     E=FqE = \frac{F}{q}
    • Substituting Coulomb's law into the intensity formula gives the magnitude of EE at distance rr from point charge +Q+Q or −Q-Q:     E=14πε0Qr2E = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r^2}
    • Expressed using Coulomb's electrostatic constant k=14πε0k = \frac{1}{4\pi\varepsilon_0}:     E=kQr2E = \frac{k Q}{r^2}