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A current in a flat circular coil produces a magnetic field.
A student suggests that the strength $B$ of the magnetic field is related to the distance $x$ from the centre of the coil (see Fig. 1.1) by the equation $B = B_0 e^{-px}$
where $B_0$ is the strength of the magnetic field for $x = 0$, and $p$ is a constant.
Design a laboratory experiment that uses a Hall probe to investigate the relationship between $B$ and $x$. You should draw a diagram showing the arrangement of your equipment. In your account you should pay particular attention to
(a) the procedure to be followed,
(b) the measurements to be taken,
(c) the control of variables,
(d) the analysis of the data,
(e) the safety precautions to be taken.
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500
543
A student is investigating how the period $T$ of a simple pendulum depends on its length $l$ as shown in Fig. 2.1.
The time $t$ for 10 oscillations is recorded for a pendulum of length $l$. The period $T$ of the pendulum is determined. The procedure is then repeated for different lengths.
It is suggested that $T$ and $l$ are related by the equation $$T = 2\pi \sqrt{\frac{l}{g}}$$ where $g$ is the acceleration of free fall.
(a) A graph is plotted of $T^2$ on the $y$-axis against $l$ on the $x$-axis. Express the gradient in terms of $g$. [1]
(b) Values of $l$ and $t$ are given in Fig. 2.2.
Calculate and record values of $T$ and $T^2$ in Fig. 2.2. Include the absolute uncertainties in $T^2$. [3]
(c) (i) Plot a graph of $T^2 / s^2$ against $l / cm$. Include error bars for $T^2$. [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 uncertainty in your answer. [2]
(d) Using your answer to (c)(iii), determine the value of $g$. Include the absolute uncertainty in your value and an appropriate unit. [3]
(e) (i) Using your answer to (d), determine the value of $l$ that is required to give a period of 1.0 s. [1]
(ii) Determine the percentage uncertainty in your value of $l$. [1]
562
527
543
