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A student is investigating the force between two charged metal spheres S and T, as shown in Fig. 1.1.
[Image_1: Diagram of spheres S and T with distance r]
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.
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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
$$\frac{s^2}{s^2 + D^2} = 4N^2\lambda^2$$
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 = ......................................................... [1]
(b) Values of $\lambda$ and $s$ are given in Fig. 2.2.
Calculate and record values of $\frac{1}{\lambda^2} / 10^{12} m^{-2}$ and $\frac{1}{s^2} / m^{-2}$ in Fig. 2.2.
Include the absolute uncertainties in $\frac{1}{s^2}$. [2]
(c) (i) Plot a graph of $\frac{1}{s^2} / m^{-2}$ against $\frac{1}{\lambda^2} / 10^{12} m^{-2}$.
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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