You will be surprised by how easy the excess electron calculations are! However, the orders of magnitude involved are not straightforward: that's where Omni's excess electrons calculator comes in handy.

We also added a brief theoretical introduction, where you will learn:

  • What is the electron and the electric charge;
  • How do we calculate excess electrons; and
  • A simple experiment to test the formula for calculating excess electrons.

We promise it will be an electrifying journey!

Before calculating excess electrons: electrons and the charge of an object

Have you ever got a spark from one of your friends? No, not in that way; we are talking of physics! Sparks are a consequence of the accumulation of charge on an object.

But... what is charge? Charge — short for electric charge — is a property of matter that describes how much an object feels the effects of an electric field. This definition may be unsatisfactory, but we know: charge is a fundamental property, as is mass, and this makes it pretty hard to find a way to define it without using some degree of redundancy or leaving something "untold".

Even though the charge may be a bit mysterious, its origin is straightforward to explain: we are talking of electrons. Electrons are elementary subatomic particles, which means that we can't break them into smaller pieces, carrying what we call unitary charge. Scientists are pretty sure that the charge of an electron is the smallest one that can live "free".

In 2019, scientists fixed the value of the electron charge. Now, at least for physicists, the electron charge is something we use to measure things and not something we measure. This is its value:

e=1.602176634×1019 C\mathrm{e} = 1.602176634\times10^{−19}\ \mathrm{C}

We measure this quantity in coulombs, the measurement unit for charge.

Every electric charge in the universe is an integer multiple of the charge of an electron; this makes the calculations for the excess electrons' number easy matter, if not for a small detail: the charge of an electron is incredibly small!

🔎 Scientists say that the electric charge is quantized. In physics, calculating the excess electrons is a simple exercise of quantum mechanics!

Electrons are small but essential. Learn more about them with Omni: try our electron speed calculator or our volt to electronvolt calculator to see other situations where we meet one of our favorite elementary particles!

How do I calculate the excess electrons number?

To calculate the excess of electrons, you need only to know the charge of your object. You can measure this quantity in various ways, even though the instrument is always called an electrometer. Once you know this quantity, in coulombs, apply the formula to calculate the excess electrons:

ne=Qe,n_{\mathrm{e}} = \frac{Q}{\mathrm{e}},

where:

  • nen_{\mathrm{e}} — Calculated number of excess electrons;
  • QQ — Charge of the object; and
  • e\mathrm{e} — Electron charge.

How do I calculate the charge from the excess electrons?

You can also calculate the charge from the excess electrons, and it's as easy as the inverse operation! If you know the number of excess electrons, calculate the coulombs with the following formula:

Q=ne×eQ = n_{\mathrm{e}} \times\mathrm{e}

An experiment: how to calculate the number of excess electrons at home

You've learned how to calculate the excess or deficit of the number of electrons. Can you apply this formula in real life? Yup! Let's see how!

Experiment set-up

  1. Gather the material:
    • An inflated balloon;
    • A woolen cloth;
    • A sheet of paper with a known weight; and
    • A ruler.
  2. Measure a square of paper with side l=1 cml = 1\ \mathrm{cm}. We know the weight of this square! If our sheet is rated, for example, 80 g/m280\ \mathrm{g/m^2}, we can calculate:
ms=80 g/m20.0001 m2=0.008 g\qquad \begin{split} m_{\mathrm{s}} &= 80\ \mathrm{g/m^2} \cdot 0.0001\ \mathrm{m^2} \\ &= 0.008\ \mathrm{g} \end{split}
  1. Place the paper on a flat surface and the ruler, vertical, in the background.
  2. Charge the balloon: rub its surface with the cloth for a few seconds. This will deposit/remove electrons from the surface.

Execution

  1. Move the balloon slowly closer to the piece of paper. At a given height, the piece of paper will "take off" and connect to the balloon. Annotate the distance between the balloon and the paper piece when this happens For us, this happened at 2 cm2\ \mathrm{cm}.

Sciencing the results!

What did we measure in this experiment? The distance at which the gravitational force acting on the piece of paper gets surpassed by the electrostatic attraction between paper and balloon.

The magnitude of the gravitational force is:

Fg ⁣= ⁣m ⁣ ⁣g ⁣= ⁣0.008 kg ⁣ ⁣9.81 m/s2=0.07848 N\begin{split} F_{\mathrm{g}}& \!= \!m\!\cdot\! g \!=\! 0.008\ \mathrm{kg}\! \cdot \!9.81\ \mathrm{m/s^2} \\ &= 0.07848\ \mathrm{N} \end{split}

🔎 You can learn how to calculate this quantity by cross-checking our two related tools, the gravitational force calculator and the acceleration due to gravity calculator!

Now, let's do the electrostatic part! Check our Coulomb's law calculator to find the formula for the electrostatic force.

Fe=kQBQPr2,F_{\mathrm{e}} = k\frac{Q_{\mathrm{B}}\cdot Q_{\mathrm{P}}}{r^2},

where:

  • kkCoulomb constant.
  • QBQ_{\mathrm{B}} and QPQ_{\mathrm{P}}Charge on, respectively, the balloon and the piece of paper. Due to the rules of induction (learn more about them at our solenoid inductance calculator), we can assume that QB=QPQ_{\mathrm{B}}= Q_{\mathrm{P}}; and
  • rr — Distance between paper and balloon.

Hence:

Fe=kQB2r2F_{\mathrm{e}} = k\frac{Q_{\mathrm{B}}^2}{r^2}

Isolate QBQ_{\mathrm{B}}, then, assuming the situation Fg=FeF_{\mathrm{g}}=F_{\mathrm{e}}, calculate its value:

QB=Fer2kQB=Fgr2k=mgr2k\begin{split} Q_{\mathrm{B}} &=\sqrt{\frac{F_{\mathrm{e}}\cdot r^2}{k\cdot Q_{\mathrm{B}}}}\\[1.2em] &=\sqrt{\frac{F_{\mathrm{g}}\cdot r^2}{k}}\\[1.2em] &=\sqrt{\frac{m\cdot g\cdot r^2}{k}}\\ \end{split}

Substitute the known values:

QB=mgr2k ⁣ ⁣ ⁣ ⁣ ⁣ ⁣ ⁣ ⁣=0.07848N(0.02 m)28.99 ⁣× ⁣109 kg ⁣ ⁣m2/(s4 ⁣ ⁣A2) ⁣ ⁣ ⁣ ⁣ ⁣ ⁣ ⁣ ⁣=5.91 ⁣× ⁣108 C\begin{split} Q_{\mathrm{B}}& =\sqrt{\frac{m\cdot g\cdot r^2}{k}}\\[1.2em] &\!\!\!\!\!\!\!\!=\sqrt{\frac{0.07848\mathrm{N}\cdot (0.02\ \mathrm{m})^2}{8.99\!\times\!10^9\ \mathrm{kg\!\cdot\! m^2/(s^4\!\cdot\! A^2)}}}\\[1.2em] &\!\!\!\!\!\!\!\!=5.91\!\times\!10^{-8}\ \mathrm{C} \end{split}

Apply the formula to calculate the number of excess electrons:

ne=Qe=5.91×108 C1.602176634×1019 C=368.9×109\begin{split} n_{\mathrm{e}} &= \frac{Q}{\mathrm{e}} \\[.8em] &=\frac{5.91\times10^{-8}\ \mathrm{C}}{1.602176634\times10^{−19}\ \mathrm{C}}\\[1.2em] & = 368.9\times10^9 \end{split}

Or, if you don't like scientific notation:

ne=368, ⁣900, ⁣000, ⁣000n_{\mathrm{e}}= 368,\!900,\!000,\!000

A bit more than a third of a trillion electrons. That's a lot, but remember, they are also pretty small!

FAQ

How do I calculate the excess or deficit number of electrons?

To calculate from coulomb to excess of electrons (or deficit), you need to follow a few simple steps:

  1. Write down the charge of an electron:
    e = 1.602176634 × 10−19

  2. Measure the charge Q of the desired object. You can do it with an electrometer.

  3. Divide Q by the charge of a single electron. The result is the number of electrons (missing or added):

    n = Q/e

Notice that a negative charge corresponds to an excess of electrons only if you consider e to be negative.

How many electrons are on a balloon if I charge it?

Around 6 trillion electrons are added to an object when you charge it by rubbing it with a cloth.

You can calculate this value by knowing that the charge we can measure on such objects in the order of the microcoulomb, Q = 1 × 10-6 C. Apply the formula to calculate the number of excess electrons to find the number of particles:

n = Q/e = 1 × 10-6/1.602176634 × 10−19 = 6.2412

What is the consequence of an excess or deficit of electrons?

An excess or deficit of electrons causes an object to be charged. A charged object displays many properties and is subjected to phenomena different than the ones relative to neutral bodies.

  • A charged object feels the effect of an electric field, either being attracted or repelled by it.

  • A charged object can emit sparks if the charge is high enough to "break" the surrounding insulator.

A small shock is one of the ways you can perceive an excess of electrons!

Why does my fleece blanket spark?

The rubbing between your body and the blanket causes many electrons to be transferred, thus causing the development of a relatively high excess charge on the blanket and an equal charge with the opposite sign on your body.

If you get close enough to the blanket with an exposed part of your body, the electrons you exchange with the blanket will return to the original object through a spark. But only if the potential difference between the two parts is high enough to ionize the air between them.

Davide Borchia
Charge (Q)
C
Number of excess electrons (N)
×10¹²
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