Question

How do you find $r$ in Coulomb’s Law?

Answer 1

Try to figure out the quantities on which Coulomb’s Law depends. The sign of the charges and the direction of the force plays a crucial role. Coulomb’s Law applies to static charges only. There are two forms of the law: scalar and vector. The scalar form gives the magnitude of the force whereas vector form gives magnitude with direction.

Complete step by step solution:
Coulomb’s Law states that the electrostatic force between two stationary and electrically charged point particles is directly proportional to the product of the magnitude of the charges and is inversely proportional to the square of the distance between them.
$F=\dfrac{1}{4\pi {{\varepsilon }_{0}}}\dfrac{{{q}_{1}}\times {{q}_{2}}}{{{r}^{2}}}$
Where
$F$ = Electrostatic force in Newton
${{q}_{1}}\And {{q}_{2}}$ = Magnitude of charges in coulomb
$r$ = distance between the charges in meters.
$\dfrac{1}{4\pi {{\varepsilon }_{0}}}=k=9\times {{10}^{9}}N.{{m}^{2}}.{{C}^{-2}}$
The direction of force is along the line joining the point charges. If both the charges involved have different signs, then the force is attractive. If the sign of the charges are same (i.e. either positive or negative) then the force is repulsive.
Here ${{\varepsilon }_{0}}$ is the permittivity of free space. It is a physical constant which represents the capability of vacuum to permit the electric fields. If there is another medium between the charges other than air then the permittivity of the medium is commonly denoted by$\varepsilon$. As force is inversely proportional to permittivity, if a medium is introduced between the charges it will affect the magnitude of the force.
Now, to find the distance between the charges, other unknown factors such as magnitude of force and the charges should be known or given. Also, the unit of each factor is important while calculating the distance between the charges ($r$). Converting the units in its standard form before solving the question will give a perfect result. Moreover, the distance between the charges is measured from the center of the charges and not from the surface as they are point charges.

Note: Coulomb’s Law is applicable only to stationary point charges. It also follows inverse square law and force under this law will also conservative in nature and it is also called central force acting between charge particles. This law is not applicable to large bodies and large charged plates.