The method and the results are on the electric potential lab. Do the analysis yourself first, then check the answers below.
Quick answer: Electric potential is potential energy per unit charge, V = U/q, measured in volts. These answers go with the AP Physics C lab on electric potential: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
The answers use the sample data. Your own numbers will vary, but the gradient should be close to the battery voltage divided by the electrode separation and the sideways readings should be nearly equal.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:E&M Unit 9
Question 1 Plot the graph
The points lie close to a straight line sloping downward from 4.9 V at 4 cm to 1.3 V at 16 cm, so V decreases linearly with x.
Question 2 Gradient and field
Gradient = (1.3 − 4.9)/(0.16 − 0.04) = −3.6/0.12 = −30 V/m, so E ≈ 30 V/m, from E = −dV/dx.
Question 3 Direction of E
V falls as x increases, so the field points along +x, away from the + electrode toward the − electrode.
Question 4 Compare with theory
Voltage/separation = 6.0/0.20 = 30 V/m. The measured 30 V/m agrees with the expected 30 V/m to within the scatter of the data.
Question 5 Equipotential check
V is the same, within 0.1 V, 2 cm either side of the centre line, so the line of constant potential runs across the tray, perpendicular to E.
Question 6 Uncertainty
Fractional uncertainty in ΔV is 0.14/3.6 = 4 % and in Δx is 0.003/0.12 = 2.5 %, giving about 5 %, so E = 30 ± 2 V/m.
Question 7 Reducing error
A longer tray makes the central region more uniform, and a probe held in a clamp removes hand movement. Reading each point three times and averaging reduces random scatter.
