The method and the results are on the gauss's law lab. Do the analysis yourself first, then check the answers below.
Quick answer: Electric flux is Φ = ∮E · dA, the field passing through a surface. These answers go with the AP Physics C lab on gauss's law: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
Model answers use the sample data in the table. Your points should lie close to a straight line through the origin, and the charge on the ball will be of the order of nanocoulombs. State the uncertainty and mention that charge leakage can curve the line.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:E&M Unit 8
tanθ = x / √(L² − x²) = 0.100 / √(0.360 − 0.0100) = 0.100 / 0.5916 = 0.169, as in the table.
Question 2 Why E = V/d
A Gaussian pillbox around the surface of one plate encloses charge σA and has flux EA only through the face in the gap, so E = σ/ε₀. The field is the same everywhere between the plates, so V = E d and E = V/d.
Question 3 Equilibrium condition
Forces on the ball: tension T, weight mg and electric force qE. Resolving, T cosθ = mg and T sinθ = qE. Dividing, tanθ = qE / (mg).
Percentage in x = 2/125 = 1.6 %. The gradient depends on the same readings, so the charge is uncertain by about 2 %, plus any error in d and in the ball mass.
Question 7 Improving the experiment
The charge leaks away in humid air and edge effects make the field non-uniform near the plate edges. Work in dry air, charge the ball just before the run and use larger plates with the ball near the centre.
