Q. An object $A$ has a charge of $- 2\mu\ C$ and the object $B$ has a charge of $+ 6\ \mu\ C$. Which statement is true?
A) $F_{AB} = - 3F_{BA}$
B) $F_{AB} = - F_{BA}$
C) $3F_{AB} = - F_{BA}$
D) $F_{AB} = 4F_{BA}$
Explanation
(b) Vector from of Coulomb’s law states that $\mathbf{F}_{AB}\ $and $\mathbf{F}_{BA}$ are equal and opposite.
Since, ${\widehat{\mathbf{r}}}_{AB\ }and\ {\widehat{\mathbf{r}}}_{BA}$ are unit vectors pointing in opposite direction, we have
$\ \ \ \ \ \ \ \ \ \ \ \ \ {\ \widehat{\mathbf{r}}}_{AB\ } = \ - {\widehat{\mathbf{r}}}_{BA}$
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Therefore, equations of force is
Given by
$\mathbf{F}_{AB} = \frac{1}{4\pi\varepsilon_{0}}\frac{q_{1}q_{2}}{r^{2}}({\widehat{\mathbf{r}}}_{AB})$
$\ \ = - \frac{1}{4\pi\varepsilon_{0}}\frac{q_{1}q_{2}}{r^{2}}{\widehat{\mathbf{r}}}_{BA} = - \mathbf{F}_{BA}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.