Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
A charge of $8 \mathrm{mC}$ is located at the origin. Calculate the work done in taking a small charge of $-2 \times 10^{-9} \mathrm{C}$ from a point $P(0,0,3 \mathrm{~cm})$ to a point $Q(0,4 \mathrm{~cm}, 0)$ via a point $R(0,6 \mathrm{~cm}, 9 \mathrm{~cm})$.
PhysicsElectrostatic Potential and Capacitance
Solution:
1937 Upvotes Verified Answer
Let $\vec{r}_1$ and $\vec{r}_2$ are the position vectors for points $P$ and Q then
$\overrightarrow{\mathrm{r}}_1=3 \hat{\mathrm{k}}$ and $\mathrm{r}_1=3 \mathrm{~cm}=0.03 \mathrm{~m}$
$\overrightarrow{\mathrm{r}}_2=4 \hat{\mathrm{j}}$ and $\mathrm{r}_2=4 \mathrm{~cm}=0.04 \mathrm{~m}$
Position of point $\mathrm{R}$ does not affect the result.
Also $\mathrm{q}=8 \mathrm{mC}=8 \times 10^{-3} \mathrm{C}$.
By formula, $\mathrm{V}=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{q}}{\mathrm{r}}$
For point $\mathrm{P}$,
$$
\mathrm{V}_1=\frac{9 \times 10^9 \times 8 \times 10^{-3}}{0.03}=24 \times 10^8 \mathrm{~V}
$$
For point $Q$,
$$
\mathrm{V}_2=\frac{9 \times 10^9 \times 8 \times 10^{-3}}{0.04}=18 \times 10^8 \mathrm{~V}
$$
Potential difference, $\left(\mathrm{V}_2-\mathrm{V}_1\right)$
$$
=18 \times 10^8-24 \times 10^8=-6 \times 10^8 \mathrm{~V}
$$
Work done $\mathrm{W}=$ charged moved $\times$ potential difference, $=\left(-2 \times 10^{-9}\right)\left(-6 \times 10^8\right)=1.2 \mathrm{~J}$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.