A charge of \( 9\,\mu\mathrm{C} \) is given a displacement \( \vec{r} = (4\hat{\imath} + 5\hat{\jmath})\,\mathrm{m} \) in an electric field \( \vec{E} = (5\hat{\imath} + 4\hat{\jmath})\,\mathrm{N/C} \). The work done in the process is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 3.6\times10^{-4}\,\mathrm{J} \)
The work done by the electric force on a charge \( q \) displaced by \( \vec{r} \) in a uniform field is \( W = \vec{F}\cdot\vec{r} = q\,\vec{E}\cdot\vec{r} \). The dot product multiplies the matching components.
\( \displaystyle \vec{E}\cdot\vec{r} = (5)(4) + (4)(5) = 40\,\mathrm{N\,C^{-1}\,m} \)
\( \displaystyle W = q\,(\vec{E}\cdot\vec{r}) = 9\times10^{-6} \times 40 = 3.6\times10^{-4}\,\mathrm{J} \)