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A student is investigating the motion of magnets falling through a vertical copper pipe as shown in Fig. 1.1.
The student releases a magnet above the copper pipe. The magnet has speed $v$ as it leaves the pipe.
It is suggested that the relationship between $v$ and $B$ is
$$v = V_0 e^{-\lambda B}$$
where $B$ is the magnetic flux density at the poles of the magnet and $V_0$ and $\lambda$ are constants.
Design a laboratory experiment to test the relationship between $v$ and $B$. Explain how your results could be used to determine values of $V_0$ and $\lambda$. 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 a circuit containing capacitors.
A capacitor of capacitance $Y$ is charged by connecting it to a power supply. The charge is shared with another capacitor of capacitance $C$ connected between the terminals P and Q, as shown in Fig. 2.1.
A voltmeter is used to measure the maximum potential difference $V$ between P and Q.
The experiment is repeated by adding additional capacitors, each of capacitance $C$, in series between P and Q.
The total capacitance $X$ between P and Q may be determined by the equation $$X = \frac{C}{n}$$ where $n$ is the number of capacitors in series.
It is suggested that $V$ and $X$ are related by the equation $$YE = (X + Y)V$$ where $E$ is the e.m.f. of the power supply.
(a) A graph is plotted of $\frac{1}{V}$ on the $y$-axis against $X$ on the $x$-axis.
Determine expressions for the gradient and $y$-intercept.
gradient = .........................................................
y-intercept = ......................................................... [1]
(b) Values of $n$ and $V$ are given in Fig. 2.2.
Data: $C = (2.7 \pm 0.4) \times 10^{-3} F$
[Table_1]
Calculate and record values of $X/10^{-3} F$ and $\frac{1}{V}/V^{-1}$ in Fig. 2.2.
Include the absolute uncertainties in $X$. [3]
(c)
(i) Plot a graph of $\frac{1}{V}/V^{-1}$ against $X/10^{-3} F$.
Include error bars for $X$. [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 $E$ and $Y$. Include an appropriate unit for $Y$.
$$E = ......................................................... V$$
$$Y = ......................................................... $$ [2]
(ii) Determine the percentage uncertainty in $Y$.
percentage uncertainty in $Y$ = ......................................................... % [1]
560
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547
