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. $3F_{AB}=-F_{BA}$
• D. $F_{AB}=4F_{BA}$

Answer 1

Answer: (B)

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

Therefore, equations of force is given by
${\vec{F}}_{AB}=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}\left({\hat{r}}_{AB}\right)$
$=-\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}{\hat{r}}_{BA}=-{\vec{F}}_{BA}$