Topic 7: Electric and Magnetic Fields — Edexcel A-Level Physics
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Topic 7: Electric and Magnetic Fields explained
A point charge or charged sphere produces a radial field, and the potential at distance r from its centre is V = Q/(4πε₀r).
Read the full explanation
Here Q is the charge in coulombs, r is the distance from the centre in metres, and ε₀ is the permittivity of free space, approximately 8.85 × 10⁻¹² F m⁻¹. The potential falls as 1/r, unlike the field strength which falls as 1/r². For example, a charge of 2.0 × 10⁻⁹ C at 0.30 m gives V = (2.0 × 10⁻⁹)/(4π × 8.85 × 10⁻¹² × 0.30) ≈ 60 V. The potential is positive near a positive charge and negative near a negative charge, and is taken as zero at infinity.
Your focus
- Apply V = Q/(4πε₀r) to calculate the potential at a point in a radial field.
- Rearrange the equation to find Q or r when the other quantities are known.
- Use the correct value of ε₀ and give the potential with the correct sign and unit.
Topic 7: Electric and Magnetic Fields exam tips
Marking Points
- States V = Q/(4πε₀r) and identifies V as electric potential in V, Q as charge in C, r as distance from the centre in m and ε₀ as permittivity of free space.
- Uses the correct value of ε₀, approximately 8.85 × 10⁻¹² F m⁻¹, and the full 4π factor.
- Converts r to metres and Q to coulombs before substitution.
- Rearranges to Q = 4πε₀rV or r = Q/(4πε₀V) when a different quantity is the unknown.
- Gives the answer with the correct sign for a positive or negative charge and the correct unit, V.
Examiner Tips
- 💡Write down ε₀ and 4π explicitly before substituting to avoid dropping the factor.
- 💡Check the sign of the potential against the sign of the charge.
- 💡Keep r in metres and Q in coulombs, and quote the answer to two or three significant figures.
Common Mistakes
- Omitting the 4π factor and using only ε₀ in the denominator; the correction is to include the full 4πε₀.
- Using the 1/r² field-strength equation E = Q/(4πε₀r²) when the question asks for potential; the correction is to use the 1/r potential equation.
- Measuring r from the surface of a charged sphere rather than its centre; the correction is to measure from the centre of the charge distribution.