This all-in-one online Coulomb’s Law Calculator performs calculations using the Coulomb’s law formula, which relates the values of two point charges and the distance between them to the value of the electric force acting on each charge. You can enter the values of any three parameters in the fields of this calculator and find the missing parameter.
F = ke· q1· q2 / r2
What Is Coulomb’s Law
One of the fundamental physical laws in the field of electrostatics is Coulomb’s Law, which describes the force of interaction between electric charges.
Coulomb’s Law, named after the French physicist Charles-Augustin de Coulomb, is a mathematical expression that defines the magnitude and direction of the electric force between two charged bodies at rest. The law states that the force of attraction or repulsion between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Coulomb’s Law is mathematically represented by the formula:
$$F = k_{e} \cdot \frac{q_1 \ q_2}{r^2},$$
where
• \(F\) is the projection of the electrostatic force vector \(\overrightarrow{F}\) on the radius-vector \(\overrightarrow{r}\) between the two point charges,
• \(q_1\) is the magnitude of the first electric charge,
• \(q_2\) is the magnitude of the second electric charge,
• \(r\) is the modulus of the radius-vector \(\overrightarrow{r}\) between the two charges (distance),
• \(k_{e}\) is the Coulomb’s constant, its value is equal to 8.98755 × 10⁹ N·m²/C².
It is important to emphasize that the above form of Coulomb’s law is a scalar one. The vector form of this law differs only in that the symbol of the force vector is used on the left, and the unit vector along the radius vector connecting two point charges is added as a factor to the right side.
In the above scalar form of Coulomb’s law, the force refers to the projection of the force vector on the radius-vector connecting the charges. The formula shows that when both charges have the same sign, the projection of the force on the radius-vector is positive. That is, in this case we are dealing with a repulsive force. When the charges have different signs, the projection of the force on the radius-vector is negative. This means that we are dealing with the force of attraction.
And of course, you need to remember that the force vector is applied to each of the charges, and the directions of these vectors are determined by the attraction or repulsion between the charges.
It is also appropriate to note here that in the case of a static system consisting of more than two charges arbitrarily located in space, it is necessary to use exclusively the vector form of Coulomb’s law.
Electric Charge and Electric Charge Units
Electric charge is a fundamental property of matter that describes the imbalance of positive and negative particles within an object. It is the basis for the existence of electric fields and electric forces.
Charged particles can be either positively or negatively charged, and objects can possess a net charge if the number of positive or negative charges is uneven. Like charges repel each other, while opposite charges attract.
Electric сharge has dimension T·I. The SI unit of electric сharge is coulomb (C). In physics and chemistry the elementary charge (e) is commonly used as a unit. In electrical engineering it is also used the ampere-hour (A⋅h).
When using our Coulomb’s Law Calculator, you can easily choose any unit of measurement that is convenient for you.
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