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A student is investigating the force between two charged metal spheres S and T, as shown in Fig. 1.1.
Each sphere may be charged by connecting the positive lead from a power supply to the sphere and then removing the lead. The electromotive force (e.m.f.) of the power supply used to charge sphere T is $V$.
The force $F$ between the two charged spheres may be determined by attaching sphere S to a top pan balance.
For a constant charge on sphere S, it is suggested that the relationship between $F$ and $V$ is
$$F = \frac{\alpha V}{r^2}$$
where $r$ is the distance between the centres of the spheres and $\alpha$ is a constant.
Design a laboratory experiment to test the relationship between $F$ and $V$. Explain how your results could be used to determine a value for $\alpha$.
You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to
- the procedure to be followed,
- the measurements to be taken,
- the control of variables,
- the analysis of the data,
- any safety precautions to be taken.
[Diagram_1]
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A student is investigating monochromatic light passing through a diffraction grating. A series of maxima are produced on a screen, as shown in Fig. 2.1.
The student measures the distance $s$ between the central maximum and the second order maximum on the screen.
The experiment is repeated for different wavelengths of light.
It is suggested that $s$ and the wavelength $\lambda$ are related by the equation $$\frac{s^2}{s^2 + D^2} = 4 N^2 \lambda^2$$ where $D$ is the distance between the diffraction grating and the screen and $N$ is the number of lines per unit length of the diffraction grating.
(a) A graph is plotted of $\frac{1}{s^2}$ on the $y$-axis against $\frac{1}{\lambda^2}$ on the $x$-axis.
Determine expressions for the gradient and $y$-intercept.
gradient = ...................................................
$y$-intercept = ...................................................
(b) Values of $\lambda$ and $s$ are given in Fig. 2.2.
[Table_1: Table of values for $\lambda/10^{-7} \text{m}$, $s/\text{m}$ and $\pm0.02$, $1/\lambda^2/10^{12} \text{m}^{-2}$]
Calculate and record values of $\frac{1}{\lambda^2}/10^{12} \text{m}^{-2}$ and $\frac{1}{s^2}/\text{m}^{-2}$ in Fig. 2.2.
Include the absolute uncertainties in $\frac{1}{s^2}$. [2]
(c) (i) Plot a graph of $\frac{1}{s^2}/\text{m}^{-2}$ against $\frac{1}{\lambda^2}/10^{12} \text{m}^{-2}$.
Include error bars for $\frac{1}{s^2}$. [2]
(ii) Draw the straight line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2]
(iii) Determine the gradient of the line of best fit. Include the absolute uncertainty in your answer.
gradient = ..................................................... [2]
(iv) Determine the $y$-intercept of the line of best fit. Include the absolute uncertainty in your answer.
$y$-intercept = .................................................. [2]
(d) (i) Using your answers to (a), (c)(iii) and (c)(iv), determine the values of $D$ and $N$. Include appropriate units.
$D$ = ..........................................................
$N$ = ........................................................... [3]
(ii) Determine the percentage uncertainty in $N$.
percentage uncertainty in $N$ = .............................. % [1]
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