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A Levels: Things to keep in mind when drawing graphs

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A. Choose a sensible scale on both axes. Do not choose an odd scale that results in a number such as 0.333 units per division, or 1 unit per 3 divisions, etc B. It is important that your plotted data point occupy more than 50% of the space provided on the graph. So, choose the axes scales accordingly. C. Label the axes with appropriate quantities and their units using the format ‘measured quantity/unit’. For instance, if you are plotting time period (\(T\)) in seconds on the y-axis and length of the pendulum in centimeters on the x-axis, then the \(y\)-axis should be labelled as ‘\(T\) / s’ and \(x\)-axis as ‘\(l\) / cm’. D. Plot all the points you have recorded in your observation table and plot them points as accurately as possible. E. Indicate points on your graph using a cross (‘✕’) instead of just a dot – because dots are hard for the reader or examiner to spot. Size of a ‘✕’ should be about the size of a small square box on the g...
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Total flux through a spherical surface enclosing an off-centered source of uniformly distributed lines

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Consider a point source \(Q\) in space from which \(N\) number of lines emanate uniformly in all directions. This source is enclosed in a spherical shell of radius \(R\) and is placed a distance \(d\) from the center of the sphere. Figure 1 (a) illustrates this arrangement. Figure 1 Let the symbol \(S\) represent the surface of the spherical shell. The flux through an infinitesimal area of the surface of the sphere is given by \[\vec{\rho}(\vec{r}) \cdot \vec{dA} \] where \(\vec{\rho}(\vec{r})\) is the density of line at a point \(\vec{r}\) on \(S\) and \(\vec{dA}\) is the infinitesimal area vector at \(\vec{r}\) on \(S\). It can be shown that the total outward flux of lines through the sphere is \[ \oint_{S} \vec{\rho}(\vec{r}) \cdot \vec{dA} = N\] Figure 1(b) illustrates the geometry of the problem, manner of placement of the coordinate system and various symbols used to represent variables in the problem. Note that the coordinate system has been chosen such that bo...
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Steps to Solving Problems

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With every iteration of this process, we develop abilities (skills) needed to process and solve complex problems that we can't learn by simply reading a theory or books. It is when we attempt to apply the theory that we truly understand and appreciate its full import. This process, however, is cognitively demanding and requires sustained effort, perseverance and motivation. 
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Combining Uncertainties I: Propagation of Errors

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PREVIOUS: Rules for Significant Figures and Rounding NEXT: Combining Uncertainties II: Application An essential component of experimentation in science is to measure the response of a physical system to the applied external stimulus. These responses, in conjunction with existing theoretical models, are used to elicit properties of the system that are not readily obvious and to construct a deeper understanding of the system's nature. The validity of understanding attained through an experiment depends on the accuracy and precision of measurements made in the experiment. Various sources of errors such as systematic errors, random errors, etc. limit the accuracy and precision, hence the reliability, of measurements. We must be mindful of these errors when making inferences based on data obtained from any experiment. Errors that creep in during measurements are fairly straightforward to figure out. It is, however, not straightforward to know how these errors ...
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How to use Latex codes in HTML environment (for Blogger, Wordpress, etc.)

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Latex is an indispensable formatting tool when it comes to writing mathematical equations. To use Latex codes in Blogger or any other blogging platform, you will need to work in HTML mode. If you are already familiar with HTML, it's a simple task. If you are not familiar with HTML, please consider investing some time into learning it. HTML a simple yet powerful tool; it gives you full control over the presentation of your content. Let's get down to it. To begin with, we first need a mechanism that would enable HTML to interpret and render Latex code. This can be done in many ways. The easiest way is to include the following line in your HTML code between <head> and </head> . <script async="" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.4/MathJax.js?config=TeX-MML-AM_CHTML" type="text/javascript"> </script> https://cdnjs.cloudflare.com houses a translator that converts Latex code into HTML synta...
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