Question

An object $A$ has a charge of $+2\, \mu C$ and the object $B$ has a charge of $+6 \,\mu C$ . Which statements is true?

• A. $ F_{AB} = − 3F_{BA} $
• B. $ F_{AB} = − F_{BA} $
• C. $ 3\,F_{AB} = − F_{BA} $
• D. $ F_{AB} = 4\,F_{BA} $

Answer 1

Answer: (B)

Vector form of Coulomb's law states that $\vec{ F }_{A B}$ and $\vec{ F }_{B A}$ are equal and opposite.
Since, $\widehat{ r }_{A B}$ and $\hat{ r }_{B A}$ are unit vectors pointing in opposite direction, we have

Therefore, equations of force is given by
$\vec{ F }_{A B}=\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}}\left(\hat{ r }_{A B}\right)$
$=-\frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}} \hat{ r }_{B A}=-\vec{ F }_{B A}$