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    Symbols, Units, and Constants

    This page provides a key to interpreting symbols and units in Introductory Electricity & Magnetism, and provides values of constants in SI units.

    Warning: Read me if you plan to copy/paste this page into your course! #copy-paste
    Because of where this page is in github, the insert components section at the top of the code is a little different. After copy/pasting this page into your course, remove one '../' from each component line at the top. All insert components statements in the text here and in the style guide have the correct path structure and do not need to be changed.

    Good luck!

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    Symbols

    Greek letters

    Symbol Name Meaning in Physics 102
    \( \gamma \) gamma Symbol for high-energy EM wave
    \( \Delta \) Delta Symbol for change in a quantity
    \( \epsilon \) or \( \varepsilon \) epsilon Electric polarizability of a material ("permittivity")
    Careful: Similar to emf symbol \( \mathcal{E} \)
    \( \theta \) theta Angle
    \( \kappa \) kappa Dielectric constant of a material
    \( \lambda \) lambda Wavelength
    \( \mu \) mu Linear (charge) density
    OR
    Magnetization in a material in a magnetic field
    \( \pi \) pi The ratio of a circle's circumference to its diameter
    \( \rho \) rho Volume (charge) density
    \( \sigma \) sigma (lower case) Area density
    or
    Blackbody radiation constant
    \( \Sigma \) Sigma (upper case) The sum of the following quantity
    \( \tau \) tau Symbol for torque
    OR
    Symbol for time constant in a circuit
    \( \phi \) phi (lower case) Angle
    \( \Phi \) Phi (upper case) Symbol for flux

    The symbol 𝛑

    Although the concept of 𝛑 has existed since at least the ancient Egyptians, the first known use of the symbol 𝛑 for its mathematical purpose was in 1706. More information on the adoption of this symbol.

    Mathematical Symbols

    This section uses the placeholder variable \( A \). You may use any relevant variable in its place.

    Symbol Meaning Use/Definition
    \( \Delta \) Change \( \Delta A =A_{final}-A_{initial} \)
    \( \sum{} \) Sum For a series of quantities \( A_1 \), \( A_2 \), \( A_3 \), etc., \( \sum A =A_{1}+A_{2}+A_{3}+\cdots \)
    \( \vec{A} \) Vector symbol The variable represents a vector quantity with magnitude and direction.
    May also be drawn with partial arrow \( \stackrel{\rightharpoonup}{A} \)
    \( |\vec{A}| \) Vector magnitude The magnitude of the vector \( \vec{A} \)
    If \( \vec{A} \) is known to be a vector, the magnitude may also be written as \( A \)
    \( A_x \) x-component of vector A The projection of the vector \( \vec{A} \) (magnitude and direction) onto the x axis.
    Similarly, \( A_y \) and \( A_z \) are the projections of \( \vec{A} \) onto the y and z axes, respectively.
    \( A_\parallel \) Parallel component notation The component of vector \( \vec{A} \) that is parallel to a second reference vector.
    \( A_\perp \) Perpendicular component notation The component of vector \( \vec{A} \) that is perpendicular to a second reference vector.
    \( A(x) \) \( A \) as a function of the variable \( x \) An expression for the value of \( A \) for any input value of the variable \( x \).
    Be careful: \( A(x) \) does not mean \( A\times x \)
    \( A_0 \) Initial value of \( A \) Typically, the value of \( A \) when \( t=0 \).
    In function format, \( A(t=0)=A_0 \)
    May be said as "A naught".
    \( \arccos(A) \)
    or
    \( \cos^{-1}(A) \)    		 Inverse cosine of \( A \)
    Similar for other trigonometric functions.    		 Inverse of the cosine function.
    Finds the value of \( \theta \) that gives \( \cos(\theta)=A \)
    May appear as "acos" on some calculators.

    Units

    You can add little cards to the side of each section. These are meant to contain extra information not critical to what's discussed in the section, such as fun-facts, extra readings related to the material, or real-world applications.

    Base Units and Unit Construction

    Physics uses SI units - that is, it constructs all units out of seconds, meters, kilograms, amperes, kelvins, and moles.

    Unit (Symbol) Quantity Construction from base units
    meters (m) Length, distance \( \mathrm{m} \)
    kilograms (kg) Mass \( \mathrm{kg} \)
    seconds (s) Time \( \mathrm{s} \)
    Newtons (N) Force \( \mathrm{kg}\frac{\mathrm{m}}{\mathrm{s^2}} \)
    Joules (J) Energy \( \mathrm{kg}\frac{\mathrm{m^2}}{\mathrm{s^2}} \)
    Watts (W) Power \( \mathrm{kg}\frac{\mathrm{m^2}}{\mathrm{s^3}} \)
    Coulombs (C) Charge \( \mathrm{A}\cdot \mathrm{s} \)
    Volts (V) Electric Potential \( \mathrm{kg}\frac{\mathrm{m^2}}{\mathrm{s}^3 \cdot \mathrm{A}} \)
    Amperes (A) Electric Current \( \mathrm{A} \)
    Ohms (\( \Omega \)) Resistance \( \mathrm{kg}\frac{\mathrm{m^2}}{\mathrm{s}^3 \cdot \mathrm{A}^2} \)
    Weber (W) Magnetic flux \( \mathrm{kg}\frac{\mathrm{m^2}}{\mathrm{s}^2 \cdot \mathrm{A}} \)
    Farad (F) Capacitance \( \mathrm{A}^2\frac{\mathrm{s^4}}{\mathrm{kg} \cdot \mathrm{m}^2} \)

    Adding Images

    You can also add images with or without a caption. For info on where images should be saved at, see the setup page. More info on formatting images is in the Style guide & documentation.

    Add caption here if you want one

    Math in physicsref

    \( \LaTeX \) can be used inside your pages. Just like in Latex, we differentiate between inline-math and display-math. One difference betweem \( \LaTeX \) and these pages is when writing math in \( \LaTeX \), you use one backslash \( (\backslash) \), but in the reference pages you need to use two \( (\backslash \backslash) \).

    Inline Math

    Inline math is math font text inside of sentences where the lines don't break. For example, \( E = mc^2 \) as proved by Einstein. This is most commonly used for variable letters like "the moment \( M \)" or units like "the units for moment are \( Nm \)".

    Display Math

    Display math is for relevant course equations. These are denoted by a different format from the surrounding text. For example, the same equation as above would look like the following.
    Mass-energy equivalence
    $$ E = mc^2 $$
    A block of equations can also be put in the same box if needed.
    Standard form of a Linear-Program. #lp-std-form
    $$ \begin{aligned}&{\text{Find a vector}}&&\mathbf {x} \\&{\text{that maximizes}}&&\mathbf {c} ^{\mathsf {T}}\mathbf {x} \\&{\text{subject to}}&&A\mathbf {x} \leq \mathbf {b} \\&{\text{and}}&&\mathbf {x} \geq \mathbf {0} .\end{aligned} $$
    When we want to show students how a particular equation is derived, we can add an expendable derivation field.
    Memorylessness of the exponential distribution. #exp-memoryless
    $$ P\left(T>s+t\mid T>s\right)=P(T>t),\qquad \forall s,t\geq 0. $$
    $$ \begin{aligned}P\left(T>s+t\mid T>s\right)&={\frac {P \left(T>s+t\cap T>s\right)}{P \left(T>s\right)}} \\ &={\frac {P \left(T>s+t\right)}{P \left(T>s\right)}} \quad \text{since} \; [0, s) \subset [0, s+t) \\ &={\frac {e^{-\lambda (s+t)}}{e^{-\lambda s}}} \\ &=e^{-\lambda t} \\ &=P(T>t).\end{aligned} $$
    Warning: Do not reuse IDs #unique-ids
    These expendable warning fields can be used to emphasize that students should really pay attention to what's inside. Here, we want to warn you not to reuse IDs, since unique IDs are essential to certain features working correctly.