Salam Academy
Sign inCreate account
Learn7408Paper 2 · Paper 2Fields and their consequencesElectric fields and uniform fields
Fields and their consequences · Subtopic 2 of 13

Electric Fields and Uniform Fields

An electric field is a region where a charge experiences a force. Field strength is the force per unit positive charge: E=FqE=\dfrac Fq (N C⁻¹ or V m⁻¹). Between parallel plates with p.d. VV and separation dd, the field is uniform: E=VdE=\dfrac Vd. A charged particle in a uniform field feels a constant force qEqE, so it accelerates uniformly and, if it enters at right angles, follows a parabola like a projectile.

Cambridge 9702 Paper 4Edexcel YPH11 WPH14AQA 7408 Paper 2≈ 35 minRevision 5 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Define electric field strength and use F=qEF=qE.
  • Draw field lines for point charges and parallel plates.
  • Use E=VdE=\dfrac Vd for parallel plates.
  • Analyse the parabolic path of a charged particle in a uniform field.
Pause and think

Gravity curves a thrown ball into a parabola. What happens to an electron fired horizontally between two charged plates?

Section 2 of 14

Core idea

Start hereSteering electrons

Old TV tubes and oscilloscopes steered beams of electrons with charged plates, bending them to draw pictures. Between two parallel plates the electric field is the same everywhere, so an electron crossing it curves exactly like a ball thrown sideways under gravity.

The big idea

E=FqE=\frac Fq; between parallel plates E=VdE=\frac Vd (uniform). A charge entering sideways follows a parabola.

1. Field between plates

Uniform field between parallel plates, and an electron beam bending
+ + + + + + +− − − − − − −e⁻
Field lines go from + to −, evenly spaced. The (negative) electron is pushed towards the + plate with constant force eEeE, so it curves in a parabola; after the plates it travels straight.
E=VdE=\frac Vd
  1. W=Fd=qEdW=Fd=qEd
    Work moving charge qq across the gap in a uniform field.
  2. W=qVW=qV
    Definition of potential difference.
  3. E=VdE=\frac Vd
    Equate; units V m−1^{-1} = N C−1^{-1}.
Worked example500 V across 2.0 cm

Field; force and acceleration of an electron.

Goal
EE, FF, aa.
Strategy
E=V/dE=V/d; F=eEF=eE; a=F/ma=F/m.
  1. E=5000.020=2.5×104 V m−1E=\frac{500}{0.020}=2.5\times10^4\text{ V m}^{-1}
    Uniform field.
  2. F=1.6×10−19×2.5×104=4.0×10−15 NF=1.6\times10^{-19}\times2.5\times10^4=4.0\times10^{-15}\text{ N}
    Force.
  3. a=4.0×10−159.11×10−31=4.4×1015 m s−2a=\frac{4.0\times10^{-15}}{9.11\times10^{-31}}=4.4\times10^{15}\text{ m s}^{-2}
    Gravity (∼10\sim10) is negligible.
Answer2.5×1042.5\times10^4 V m−1^{-1}; 4.0×10−154.0\times10^{-15} N; 4.4×10154.4\times10^{15} m s−2^{-2}.
✓ CheckElectrons are so light the acceleration is enormous ✓.
Worked exampleDeflection of the beam

Electron enters at 2.0×1072.0\times10^7 m s−1^{-1} along 5.0 cm plates.

Goal
Sideways deflection.
Strategy
Projectile: constant horizontal speed, uniform sideways acceleration.
  1. t=0.0502.0×107=2.5×10−9 st=\frac{0.050}{2.0\times10^7}=2.5\times10^{-9}\text{ s}
    Time between plates.
  2. y=12(4.4×1015)(2.5×10−9)2=1.4 cmy=\tfrac12(4.4\times10^{15})(2.5\times10^{-9})^2=1.4\text{ cm}
    From rest sideways.
Answer1.41.4 cm.
✓ Checky=eVL22mdv2y=\frac{eVL^2}{2mdv^2} gives the same 1.41.4 cm ✓. (Entering mid-way between these plates, 1 cm from each, it would actually strike one.)
Common misconceptionIncluding gravity For electrons and ions, mgmg is negligible compared with qEqE.
Pause and think

How would a proton's deflection compare?

Summary

  • E=F/q=V/dE=F/q=V/d.
  • Projectile-like paths.
Key words
Electric field strength
Force per unit positive charge.
HistoryFaraday's lines of force. Michael Faraday, who had little formal mathematics, pictured electric and magnetic effects as invisible "lines of force" filling space. Mathematicians mocked the idea at first, but James Clerk Maxwell turned it into his field equations, and fields became central to all of modern physics.
Fun factOld TVs were particle accelerators. A cathode-ray TV accelerated electrons through about 2525 kV and steered them with fields to paint the picture, line by line, 5050 times a second. Every family that owned one had an electron gun in the living room.
Keep reading for free

Create a free account to read the rest of this lesson: key formulae, worked examples, explore the graph, common mistakes, exam tip, guided practice and more. Your answers are checked and your progress is saved.

Create free accountSign in