Electric Field Of A Point Charge (Copy)

• A point charge is an idealized charge that is assumed to occupy no space (i.e. infinitely small).
• The electric field strength at a distance r from a point charge Q in free space is given by:

  E = Q / (4πε₀r²)

  Where:
  E = electric field strength (N/C or V/m)
  Q = point charge (C)
  r = distance from the charge (m)
  ε₀ = permittivity of free space = 8.85 × 10⁻¹² C² N⁻¹ m⁻²

Understanding the Equation

• E is inversely proportional to r², meaning:
  • As the distance from the point charge increases, the field strength decreases rapidly.
• The direction of E:
  • Radially outward from a positive point charge
  • Radially inward toward a negative point charge
• The electric field produced by a point charge is spherically symmetric.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Units and Definitions

• The unit of E is N/C (newton per coulomb), which is equivalent to V/m (volt per metre).
• The electric field is defined as:
  • Force per unit positive charge placed at a point in the field:
    • E = F / q

Comparison With Gravitational Field

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Graphical Representation

• E vs. r graph:
  • Shape: Hyperbola, since E ∝ 1/r²
  • As r increases, E approaches zero
  • E becomes infinitely large as r approaches zero

Electric Field Lines for a Point Charge

• A positive point charge has field lines radiating outward.
• A negative point charge has field lines directed inward.
• The density of field lines represents the strength of the field:
  • Closer lines = stronger field
  • Sparse lines = weaker field

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Worked Example

• A point charge Q = 5.0 × 10⁻⁶ C is located in free space.
  What is the electric field strength at a point 0.30 m away?

  E = Q / (4πε₀r²)
  E = (5.0 × 10⁻⁶) / (4π × 8.85 × 10⁻¹² × 0.30²)
  E ≈ 5.0 × 10⁵ N/C

Superposition Principle (Multiple Charges)

• If more than one point charge is present:
  • The net electric field at a point is the vector sum of individual electric fields from each charge.
• Requires resolving components if vectors are not aligned.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course