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What is Data Analytics?
What does a Data Analyst do? The job responsibilities of a Data Analyst are computer-based, and this work can be done remotely or in-person at the office. There can be meetings throughout the day, such as a quick meeting in the morning to discuss the current projects. It can be helpful to provide consistent updates…
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Gauss’s Law in One Dimension and in Three Dimensions
Recall the following form of Gauss’s Law from this post: $ \frac{\partial}{\partial x} E_x + \frac{\partial}{\partial y} E_y + \frac{\partial}{\partial z} E_z = \frac{\rho}{\epsilon_0 \epsilon_r} $ One Dimension If a problem is “one-dimensional” along the, say, $x$-axis, one has $ \frac{\partial}{\partial x} E_x = \frac{\rho}{\epsilon_0 \epsilon_r} $ In words: the partial derivative with respect to $x$…
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Gauss’s Law in Differential Form and Cartesian Coordinates
Gauss’s Law in Differential Form In differential form, Gauss’s Law is $ \vec{\nabla} \cdot \vec{E} = \frac{\rho}{\epsilon_0 \epsilon_r} $ The next part of this post attempts to demystify this law a bit. Description of Symbols The $\vec{\nabla}$ on the left is called ‘del’, and it can be written in terms of Cartesian unit vectors and…
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Pi
Pi, or $\pi$, is commonly used in the context of circles in geometry. In particular, the circumference $C$ of a circle that has a diameter $d$ is $C = \pi d$. Also, the area $A$ of a circle with radius $r$ is $ A = \pi r^2$. Note that $2r = d$. This is how…