Question

What is the force between two small charged spheres having charges $2\times {10}^{-7}C$ and $3\times {10}^{-7}C$ placed 30cm apart in air?

Answer 1

Let us consider two charges $q_1$ and $q_2.$ According to the question, $q_1=2\times {10}^{-7}C$ and $q_2=3\times {10}^{-7}C$



Distance (d) between $q_1$ and $q_2$ is $30cm=0.3m$
Using Coulomb's law, the force between two charges is given by
$F=\frac{1}{4\pi {\epsilon }_0}.\frac{q_1{q}_2}{d^2}$
( The charges are placed in air, k=1)
Putting the values of $\frac{1}{4\pi {\epsilon }_0},q_1,q_2$ and $d$, we get $F=\frac{9\times {10}^9\times 2\times {10}^{-7}\times 3\times {10}^{-7}}{0.3\times 0.3}=\frac{9\times 2\times 3\times {10}^{-5}}{3\times 3\times {10}^{-2}}=6\times {10}^{-3}N$
As the charges $q_1$ and $q_2$ both are positive in nature, they repel each other.