Because of surface charge density, we have a much better understanding of electricity mechanics, sensory physiology, and electric magnetism.

    Helmholtz, among just a few others, is one of the fathers of electrodynamics as we know it today.

    Here we dive into understanding what surface charge density is, what units it is measured by, and how to calculate it.

    For easy and effortless conversions between units like C/cm2 and C/in2, check out our free surface charge density calculator.


    What is surface charge density?

    Surface charge density is the total amount of charge on the entire surface area of a solid object.

    When an object is submerged in a solution containing electrolytes, it forms an outer shell that produces a charge.

    Another name for this charged object is a colloid. And this is where surface charge comes into play.

    Using the correct formula you can define the amount electric potential difference between the outer surface and inner surface of different states.

    Wait, What Are Colloids?

    Colloids aren't strictly solid items.

    They can also be formed from fluid mediums (including gases) and these can be used to reduce fluid drag in different types of electrical systems.

    In other words, surface charge density applies to any solid geometric shape and liquid, or liquid and gas. It is present on any conductive surface.

    How is surface charge density used?

    There are a couple of reasons you would use the charge density formula to find the amount of charge on a surface.

    In most cases, you want to make sure that you are able to place objects against one another.

    If each object is a conductor than the amount of surface charge could cause an unwanted reaction.

    So before placing two objects together, you would need to determine the surface charge of both for safety.

    In the event of fixed objects, there are applications that need to determine how much of an electric field exists between two objects.

    If each object has enough of a surface charge, it can create an electric field between all of the objects.

    What is the standard unit of surface charge density?

    The unit that denotes charge density is typically coulombs per square meter.

    A coulomb is defined as the standard unit of electric charge, equal to the quantity of electricity conveyed in one second by a current of one ampere.

    Put simply, it's the name for the amount of electricity created in one second.

    So, when you are measuring the entire surface's charge density you are determining how much total electricity is being conveyed across the whole entire surface in one second.

    How do you convert surface charge density units?

    So what if your initial measurements were made in coulombs per square centimeter but you need the answer in coulombs per square inch?

    C/cm2 to C/in2

    There would be 6.4516 coulombs per square inch for every 1 coulomb per square centimeter.

    Simply multiply your C/cm2 by the number above to get your C/in2 equivalent

    C/in2 to C/cm2

    There are 0.1550 coulombs per square centimeter for every one coulomb per square inch.

    Just like above, you'll multiply your C/in2 by the above factor to go back to C/cm2.

    And this is just one example. The easiest way to convert between surface charge density units is with a calculator.

    Ours allows you to convert between 6 different measurements effortlessly.

    How is surface charge density calculated?

    The total charge density can be calculated using the surface charge density equation. The formula looks like this:

    σ = q / A

    To find the answer, you take the total charge of the entire body (represented by q) and divide it by the surface area (represented by A).

    So, once you have the charge of the object and its total surface area you can find the surface charge density with ease.

    What's an example of a surface charge density?

    Example using a solid

    For the first example, let's find the surface charge density of a conductor with an area of 5 meters squared and a charge of 3 Coloumbs.


    We know that:

    • Charge (q) = 3 C
    • Area (A) = 5 m2


    σ = q / A

    σ = 3 / 5

    σ = 0.6 C/m2

    Example using a sphere

    For the second example, let's find the surface charge density of a sphere with a radius of 2 centimeters and a charge of 8 Coloumbs.


    First, recall the equation to find the area of a sphere (A = 4 pi r2).

    We know that:

    • Charge (q) = 8 C
    • Area (A) = 50.27 (See the equation below for how we got there)


    Next, plug that into your formula including the other necessary variables.

    σ = q / A

    σ = q / (4 pi r2)

    σ = 8 / (4 pi 22)

    σ = 8 / 50.27

    σ = 0.1591 C/cm2

    When was surface charge density discovered?

    One of the first scientists to suggest the existence of surface charge and surface charge density was a German physicist named, Hermann von Helmholtz.

    After becoming a physics professor, he started making discoveries and writing theorems.

    Believe it or not, when Hermann Von Helmholtz began his work and started publishing theories on electrodynamics in 1870, scientists had yet to accept one electrical theory.

    Everyone was still shooting for the moon, taking guesses about how all this worked.

    Maxwell, F. E. Neuman, and Weber were all competing in the game of discovering how electrodynamics worked.

    Helmholtz was the first to develop agreed-upon formulas for electrodynamics.

    The work of these early physicists paved the way for our current understanding of electricity and how it interacts with the surfaces around us.

    It has allowed us to harness the power and make it work for us.

    Because of this early work we are now able to determine these values with preconstructed formulas.

    Final words?

    At the end of the day, surface charge density can be found very simply with a straightforward formula.

    You only need to know a few elements of the object involved to find the entire surface charge. And hopefully, you got everything you needed from this guide.

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