Question

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

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

$E=\dfrac{k{{Q}_{1}}{{Q}_{2}}}{{{r}^{2}}}$
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 $F=9\times {{10}^{9}}N$.