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# Define one coulomb on the basis of coulomb’s law.

Last updated date: 13th Jun 2024
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Hint: Coulomb’s law can be given as “The electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects.” Which can be given mathematically as, $E=\dfrac{k{{Q}_{1}}{{Q}_{2}}}{{{r}^{2}}}$. Using this we will define one coulomb.

Formula used:
$E=\dfrac{k{{Q}_{1}}{{Q}_{2}}}{{{r}^{2}}}$

Before defining coulomb we will define coulomb’s law which can be stated as, “The electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects.” which can be given mathematically as,

$E=\dfrac{k{{Q}_{1}}{{Q}_{2}}}{{{r}^{2}}}$

Where k is constant, Q is charge and r is distance between two charges.
Now, for finding one coulomb charge we have to consider the distances between two charges as $1\ m$, value of k is $9\times {{10}^{9}}$ and to equal charges of opposite charges are considered. And the force acting is $F=9\times {{10}^{9}}N$. Substituting these values, we will get,

$9\times {{10}^{9}}=\dfrac{9\times {{10}^{9}}Q}{{{\left( 1 \right)}^{2}}}\Rightarrow Q=1C$

From, this we can say that the one coulomb can be defined as the quantity of charge, which when placed at a distance $1\ m$ in vacuum or air from an equal charge, experiences a repulsive force $F=9\times {{10}^{9}}N$.

Note:
In this we have considered the like charges so the net force remains zero as the direction of forces are also opposite, but if we consider the unlike charges as then the attraction force will be towards one of the charges so, if we change the value of Q the answer will change which is wrong. So, students must consider the charges repulsive to get the answer.