Paper 4 Electric Fields Answers

Q1 Potential Gradient Between Parallel Plates

1. Axes correctly oriented and labelled with units [1]; sensible linear scales using most of the grid [1]; all seven points plotted accurately [2]; single best-fit straight line drawn [1].

2. A large triangle on the best-fit line gives, for example,

   $$\left|\frac{\Delta V}{\Delta x}\right|\approx \frac{12.1}{6.0}=2.02{\text{V cm}}^{-1}.$$

   Since $\vec{E}=-\nabla V$, the magnitude is

   $$E\approx 2.02\times 10^2{\text{V m}}^{-1}.$$

   Accept values consistent with the candidate’s best-fit line, with correct conversion from centimetres to metres. [3]

3. The points lie close to a straight line, so the potential gradient—and hence $E$—is approximately constant. [2]

4. Near a finite plate’s edge, field lines spread out (fringing), so the field is not uniform and $E\ne V/d$ locally. [2]

Q2 Measuring Plate Field

1. Measure p.d. $V$ across the plates and separation $d$, then use $E=V/d$ for the central uniform region. [2]
2. Switch off before changing connections, use insulated leads, or avoid touching exposed conductors. [1]
3. The plates are finite, so field lines spread and curve near their edges (fringing); consequently the potential gradient is not constant there. [2]