Question: Q. 3. (i) Use Gauss’s theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet with surface charge density
(ii) An infinitely large thin plane sheet has a uniform surface charge density $+\sigma$. Obtain an expression for the amount of work done in bringing a point charge $q$ from infinity to a point, distant $r$, in front of the charged plane sheet -
R] [OD II, 2017]
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Solution:
Ans. (i) Similar to Q. 7, Short Answer Type II 3
(ii) Amount of work done:
$$ \begin{align*} & W=q \int_{\infty}^{r} \vec{E} \cdot d \vec{r} \ & W=q \int_{\infty}^{r}(-E . d r) \ & W=-q \int_{\infty}^{r}\left(\frac{\sigma}{2 \varepsilon_{0}}\right) d r \ & W=\frac{q \sigma}{2 \varepsilon_{0}}|\infty-r|=\infty \end{align*} $$
[CBSE Marking Scheme, 2017]
