Uniform Electric Fields (Copy)

• A uniform electric field is a region where the electric field strength is constant in both magnitude and direction throughout the field.
• This type of field is typically created between two large, parallel conducting plates that have a constant potential difference across them.
• The field lines in a uniform electric field:
  • Are parallel and equally spaced.
  • Indicate that the electric force experienced by a test charge is the same everywhere between the plates.

• The electric field strength E in a uniform field is given by:
  • E = ∆V / ∆d
  • Where:
    ∆V = potential difference between the plates (V)
    ∆d = separation between the plates (m)
    E = electric field strength (V/m or N/C)
• This equation comes from the definition of electric field in a uniform field:
  • It shows how the field strength is the potential change per metre of separation between plates.

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

Motion of Charged Particles in a Uniform Electric Field

• When a charged particle enters a uniform electric field:
  • It experiences a constant force in the direction of the field (for a positive charge) or opposite (for a negative charge).
  • This constant force causes uniform acceleration.
  • Force on the particle:
    F = qE
    Where:
    q = charge on particle (C)
    E = electric field strength (N/C)
    F = electric force (N)
• The acceleration of the charged particle is:
  a = F / m = qE / m
  Where:
  m = mass of the particle (kg)
• This motion is similar to projectile motion if the field is vertical and the particle enters horizontally.

• Example:
  A proton (charge = 1.60 × 10⁻¹⁹ C, mass = 1.67 × 10⁻²⁷ kg) is placed in an electric field of strength 2.0 × 10⁴ N/C.
  Find the acceleration of the proton:
  a = qE / m = (1.60 × 10⁻¹⁹ × 2.0 × 10⁴) / (1.67 × 10⁻²⁷) = 1.92 × 10¹² m/s²

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

• If a charged particle enters the uniform field with a velocity perpendicular to the field:
  • It will undergo uniform acceleration in the direction of the field.
  • It creates a parabolic trajectory, similar to projectile motion under gravity.
• If the initial velocity is along the field (parallel):
  • The particle accelerates or decelerates in a straight line, depending on the sign of the charge.
• This behaviour allows us to control and deflect charged particles using electric fields — a principle used in:
  • Cathode ray tubes
  • Particle accelerators
  • Mass spectrometers
  • Inkjet printers

Summary of Key Equations in Uniform Fields:

• E = ∆V / ∆d
• F = qE
• a = qE / m
• Work done on particle = q∆V
• Kinetic energy gained = q∆V (from energy conservation)

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

Diagrammatic Understanding:

• Electric field lines: parallel and equally spaced
• Equipotential lines: perpendicular to electric field lines
• Particle trajectory:
  • Straight line for motion along field lines
  • Curved path (parabolic) for motion at an angle to field

• The electric field between two parallel plates can be used for velocity selection in combination with magnetic fields, such as in velocity selectors in mass spectrometers.
• In these systems, only particles with a specific velocity can pass through undeflected when:
  • qE = qvB → v = E / B

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