A-Level — physicsHard3 min read

Electric Fields

Coulomb's law; E = F/q; E = V/d for uniform fields; electric potential

Tutor AI Team
Tutor AI Team

# Electric Fields — A-Level Physics

Electric fields describe the region around a charged object where other charges experience a force. At A-Level, we study both uniform fields (parallel plates) and radial fields (point charges).

1. Coulomb's Law

F=14πε0Qqr2=kQqr2\boxed{F = \frac{1}{4\pi\varepsilon_0}\frac{Qq}{r^2} = \frac{kQq}{r^2}}

Where:

  • k=1/(4πε0)=8.99×109k = 1/(4\pi\varepsilon_0) = 8.99 \times 10^9 N m² C⁻²
  • ε0=8.85×10−12\varepsilon_0 = 8.85 \times 10^{-12} F/m (permittivity of free space)

Like charges repel; opposite charges attract.

2. Electric Field Strength

E=Fq\boxed{E = \frac{F}{q}}

Units: N/C or V/m.

Uniform Field (parallel plates)

E=VdE = \frac{V}{d}

Where VV = potential difference, dd = plate separation.

Radial Field (point charge)

E=14πε0Qr2=kQr2E = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2} = \frac{kQ}{r^2}

3. Electric Potential

For a point charge: V=14πε0Qr=kQr\boxed{V = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r} = \frac{kQ}{r}}

  • Positive charge: positive potential
  • Negative charge: negative potential
  • Potential is a scalar (can simply add)

Electric Potential Energy

Ep=qV=kQqrE_p = qV = \frac{kQq}{r}

4. Comparison: Gravitational vs Electric Fields

Property Gravitational Electric
Force F=GMm/r2F = GMm/r^2 F=kQq/r2F = kQq/r^2
Field strength g=GM/r2g = GM/r^2 E=kQ/r2E = kQ/r^2
Potential V=−GM/rV = -GM/r V=kQ/rV = kQ/r
Type Always attractive Attractive or repulsive
Shielding Cannot be shielded Can be shielded

5. Motion of Charged Particles in Fields

In Uniform Electric Field

  • Force F=qE=qV/dF = qE = qV/d (constant)
  • Acceleration a=qE/ma = qE/m (constant)
  • If particle enters perpendicular to field: parabolic path (like projectile motion)

Millikan's Oil Drop Experiment

At equilibrium: qE=mgqE = mg q=mg/E=mgd/Vq = mg/E = mgd/V

Millikan found charge was always a multiple of e=1.6×10−19e = 1.6 \times 10^{-19} C → charge is quantised.

Worked Example: Coulomb's Law

Problem

Two charges of +3 μC and −5 μC are 20 cm apart. Find the force.

F=kQq/r2=8.99×109×3×10−6×5×10−6/(0.2)2F = kQq/r^2 = 8.99 \times 10^9 \times 3 \times 10^{-6} \times 5 \times 10^{-6}/(0.2)^2 =8.99×109×15×10−12/0.04=0.1349/0.04=3.37= 8.99 \times 10^9 \times 15 \times 10^{-12}/0.04 = 0.1349/0.04 = 3.37 N (attractive)

Solution

Worked Example: Parallel Plates

Problem

Plates separated by 2 cm with PD of 500 V. Find field strength and force on an electron.

E=V/d=500/0.02=25,000E = V/d = 500/0.02 = 25{,}000 V/m F=qE=1.6×10−19×25000=4.0×10−15F = qE = 1.6 \times 10^{-19} \times 25000 = 4.0 \times 10^{-15} N

Solution

Worked Example: Electric Potential

Problem

Find the potential at 10 cm from a +2 μC charge.

V=kQ/r=8.99×109×2×10−6/0.1=1.80×105V = kQ/r = 8.99 \times 10^9 \times 2 \times 10^{-6}/0.1 = 1.80 \times 10^5 V = 180 kV

Solution

7. Practice Questions

    1. Calculate the force between a proton and electron at 5.3×10−115.3 \times 10^{-11} m apart. (2 marks)
    1. An electron is accelerated through 2000 V. Find its final speed (me=9.11×10−31m_e = 9.11 \times 10^{-31} kg). (3 marks)
    1. Compare gravitational and electric fields, listing three similarities and three differences. (4 marks)

    Answers

    1. F=ke2/r2=8.99×109×(1.6×10−19)2/(5.3×10−11)2=8.2×10−8F = ke^2/r^2 = 8.99 \times 10^9 \times (1.6 \times 10^{-19})^2/(5.3 \times 10^{-11})^2 = 8.2 \times 10^{-8} N.
    1. qV=12mv2qV = \frac{1}{2}mv^2. v=2qV/m=2×1.6×10−19×2000/9.11×10−31=7.03×1014=2.65×107v = \sqrt{2qV/m} = \sqrt{2 \times 1.6 \times 10^{-19} \times 2000/9.11 \times 10^{-31}} = \sqrt{7.03 \times 10^{14}} = 2.65 \times 10^7 m/s.

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Summary

  • Coulomb's Law: F=kQq/r2F = kQq/r^2
  • E=F/qE = F/q; uniform field: E=V/dE = V/d; radial: E=kQ/r2E = kQ/r^2
  • V=kQ/rV = kQ/r (scalar); Ep=qVE_p = qV
  • Charged particle in uniform field: constant acceleration, parabolic path
  • Charge is quantised: multiples of ee
Tags:
#a-level#physics#fields#electric-field#coulombs-law#electric-potential

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