Coulomb's law is a law of physics describing the electrostatic interaction between electrically charged particles. Was formulated and first published in \(1783\) by French physicist Charles Augustin de Coulomb and was essential to the development of the study of electricity. This law states that the magnitude of the force between two punctate electrical charges (\(q_1\) and \(q_2\)) is directly proportional to the product of the absolute values (modules) of the two charges and inversely proportional to the square of the distance r between them. This force can be attractive or repulsive depending on the sign of the charges. It is attractive if the charges have opposite signs. It is repulsive if the charges have the same sign.

Diagram depicting the basic mechanism of Coulomb's law. The like charges repel and opposite charges attract Once detailed measurements using a torsion balance, concluded that the Coulomb force is fully described by the following equation:

Where :

Is the Force In Newtons \((N)\) \(C^2 N^{-1} M{-2} \) Is the Permittivity of free space\(r\) Is the Distance between the Two Point charges in Meters \((m)\) and \(Q_1\) and \(Q_2\), respective load values in Coulombs \((C)\) .

Is the Vector that Indicates the Direction in Which the Electric Force points.Sometimes it replaces the factor \(\frac{1}{4 \pi \epsilon_o }\) by \(k\) , Coulomb's Constant, with \(k\)

The previous notation is a compact vector notation, which is not specified any coordinate system. If the load \(1\) is the source and the load at point \(2\) with Cartesian coordinates \((x, y, z)\) the Coulomb force takes the form:

How to charge a Coulomb (C 1) is very large, it is customary to use submultiples of this unit. Thus we have:

\(1\) Milicoulomb = \(10^{-3} C\)

\(1\) Microcoulomb = \(10^{-6} C\)

\(1\) Nanocoulomb = \(10^{-9} C\)

\(1\) Picocoulomb = \(10^{-12} C\)

Remembering that \(C= 6,25 \times 10^{18} \) Electrons

# Examples

Problem I

Two particles of electric charges

\(Q = 4.0 × 10^ {-16} C\) and \(q = 6.0 × 10^{-16} C \)

vacuum are separated by a distance of \(3,0 \times 10^{-9}m\).

Where \(k = 9.0 \times 10^9\) , the intensity of the force of interaction between them, in newtons, Is :

\(a) 1,2 \times 10{-5}\)

\(b) 1,8 \times 10{-4}\)

\(c) 2,0 \times 10^{-4}\)

\(d) 24 \times 10^{-5}\)

\(e) 30 \times 10^{-4}\)

Solution :

\(F = \frac{k \times Q_1 \times Q_2}{d^2}\)

\(F = \frac{9,0 \times 10^9 \times 4,0 \times 10^{-16} \times 6,0 \times 10^{ -16}}{(3,0 \times 10^{-9})^2}\)

\(F = \frac{9,0 \times 10^9 \times 4,0 \times 10^{-16} \times 6,0 \times 10^{-16}}{(3,0 \times 10^{-9} \times 3,0 \times 10^{-9})}\)

\(F = \frac{3,0 \times 10^9 \times 4,0 \times 10^){-16} \times 2,0 \times 10^{-16}}{10^{-18} }\)

\(F = \frac{24 \times 10^9 \times 10^{-16} \times 10^{-16}}{10^{-18} }\)

\(F = \frac{24 \times 10^{-23}}{10^{-18} }\)

\(F = \boxed{24 \times 10^{-5} N} \)

You Can Watch these Videos for See More Examples:

## Comments

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TopNewest@Gabriel Merces Fix k in the example. It is not dimensionless.

\[k=9.0\times{}10^{9} \frac{\text{ N m}^2}{\text{C}^2}\] – Bernardo Sulzbach · 2 years, 8 months ago

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interesting – Parth Lohomi · 2 years, 9 months ago

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very interesting – Shivam Shukla · 2 years, 9 months ago

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Hello, try visiting http://sciencefront.webs.com for some cool science stuff for kids... – Kshitij Khandelwal · 2 years, 9 months ago

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Really well explained – Mardokay Mosazghi · 2 years, 10 months ago

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– Gabriel Merces · 2 years, 10 months ago

Thanks ! This Is Very Important for Me !Log in to reply

i can't understand the coulomb force with cartesian coordinates – Padma Vathi · 2 years, 10 months ago

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I wonder why they define \(C=6.25\times10^{18}\) electrons. I mean for example there is a reason for \(1\text{ mol}=6.02\times10^{23}\), but what about Coulomb? I hope I'm not asking silly questions... – Christopher Boo · 2 years, 10 months ago

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\(1\) Coulomb is the Amount of Electric Charge carried by the Current of \(1\) ampere per \(1\) second.

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– Christopher Boo · 2 years, 10 months ago

So I've just misunderstood the definition of Coulomb, Thanks!Log in to reply

– Christopher Boo · 2 years, 10 months ago

By the way, great note!Log in to reply

@Christopher Boo Sorry this is off topic but how did you find brilliant squared? Satisfactory? – Mardokay Mosazghi · 2 years, 10 months ago

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– Christopher Boo · 2 years, 10 months ago

Well, at first I thought the Practice Maps will be great, then it turns out well too! And the save sets feature is awesome! :)Log in to reply