Electric Fields (Copy)

A2 Level Physics – Section 18: Electric Fields and Potential (Detailed Notes)

18.1 Electric Fields and Field Lines

1. Definition of Electric Field

• An electric field is a region where a charge experiences a force.
• It is a field of force, acting at a distance.
• Electric field strength (E) = force per unit positive charge:
  E = F / q
• Unit: N/C or V/m

2. Force on a Charge in an Electric Field

• F = q·E
  • F = force (N)
  • q = charge (C)
  • E = electric field strength (N/C)
• Direction of force:
  • On positive charge → same as field
  • On negative charge → opposite to field

3. Electric Field Lines

• Indicate the direction of force on a positive test charge
• Properties:
  • Lines point away from +ve, towards –ve charges
  • Closer lines = stronger field
  • Never cross
  • Uniform field = parallel, evenly spaced lines

18.2 Uniform Electric Fields

1. Field Between Parallel Plates

• For uniform electric fields (e.g. between parallel plates):
  E = ∆V / ∆d
  • ∆V = potential difference (V)
  • ∆d = separation between plates (m)
• Direction: from positive to negative plate

2. Motion of Charged Particles in Uniform Fields

• Charged particles experience a constant force:
  F = qE
• This causes uniform acceleration in the direction of the field (if +ve) or opposite (if –ve)
• Path:
  • Straight line if no initial velocity
  • Parabolic if particle has horizontal motion (projectile-like path)

18.3 Electric Force Between Point Charges

1. Spherical Conductors as Point Charges

• A uniformly charged sphere (or spherical conductor) acts as if all its charge is concentrated at its center, when observed from outside.

2. Coulomb’s Law

F = (1 / 4πε₀)·(Q₁·Q₂) / r²

• F = electrostatic force (N)
• Q₁, Q₂ = charges (C)
• r = separation between charges (m)
• ε₀ = permittivity of free space = 8.85 × 10⁻¹² F/m

Key Features:

• Inverse square law
• Attractive for unlike charges, repulsive for like charges

18.4 Electric Field of a Point Charge

1. Electric Field Strength Due to a Point Charge

E = (1 / 4πε₀)·(Q / r²)

• E = field strength (N/C)
• Q = source charge (C)
• r = distance from charge (m)
• Radial field:
  • Outward for positive charge
  • Inward for negative charge

18.5 Electric Potential

1. Definition of Electric Potential

• Electric potential (V) at a point:
  Work done per unit positive charge to bring a small test charge from infinity to that point

Unit: volt (V) = J/C

2. Electric Field as Potential Gradient

E = –dV / dr

• Electric field strength = negative gradient of the potential with respect to distance

3. Electric Potential Due to Point Charge

V = (1 / 4πε₀)·(Q / r)

• V = electric potential (V)
• Q = source charge (C)
• r = distance from charge (m)
• Positive for positive Q, negative for negative Q
• Potential approaches zero at infinity

4. Electric Potential Energy Between Two Charges

Eₚ = (1 / 4πε₀)·(Q·q / r)

• Eₚ = potential energy (J)
• Q, q = charges (C)
• r = distance between them (m)
• Eₚ > 0 for like charges (repel)
• Eₚ < 0 for unlike charges (attract)