IB Physics HL D.2 practice question

Question 1

Paper 2Hard10 marks

In a simplified Millikan oil-drop experiment, negatively charged drops are held stationary between parallel plates. The polarity is chosen so that the electric force on a drop is upward. Assume buoyancy and other forces are negligible. The potential difference between the plates is $400\ \mathrm{V}$ and their separation is $4.00\ \mathrm{mm}$

Drop A has mass $4.90\times10^{-15}\ \mathrm{kg}$ Further drops are measured using the same method. The uncertainty in each charge estimate, including that for drop A, is $\pm0.08\times10^{-19}\ \mathrm{C}$ An independently calibrated candidate value is $e_0=1.60\times10^{-19}\ \mathrm{C}$ treat its uncertainty as negligible.

Drop	Measured charge magnitude / $10^{-19}\ \mathrm{C}$
B	3.18
C	4.79
D	6.39
E	8.01
F	5.55

(a)

Show that the magnitude $q$ of the charge on a stationary drop is given by

q=\frac{mgd}{V},

where $m$ is the drop mass, $g$ is gravitational field strength, $d$ is the plate separation and $V$ is the potential difference.

[2]

(b)

Calculate the magnitude of the charge on drop A. Give your answer in coulombs.

[2]

(c)

Using $e_0$ and your answer to (b), determine the nearest integer $n$ for each of drops A–E, where $q\approx ne_0$

[2]

(d)

A student claims that the results for drops A–E establish that $e_0$ is the smallest possible charge, while drop F disproves charge quantization. Evaluate this claim using the measurements and their uncertainties.

[4]