Electrostatics 7 Question 27
29. There are two large parallel metallic plates $S _1$ and $S _2$ carrying surface charge densities $\sigma _1$ and $\sigma _2$ respectively $\left(\sigma _1>\sigma _2\right)$ placed at a distance $d$ apart in vacuum. Find the work done by the electric field in moving a point charge $q$ a distance $a(a<d)$ from $S _1$ towards $S _2$ along a line making an angle $\pi / 4$ with the normal to the plates.
(2004, 2M)
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Solution:
- Electric field near a large metallic plate is given by $E=\sigma / \varepsilon _0$. In between the plates the two fields will be in opposite directions. Hence,
$$ E _{\text {net }}=\frac{\sigma _1-\sigma _2}{\varepsilon _0}=E _0 \text { (say) } $$
Now, $W=(q)$ (potential difference)
$$ \begin{aligned} & =q\left(E _0 a \cos 45^{\circ}\right)=(q) \frac{\sigma _1-\sigma _2}{\varepsilon _0} \frac{a}{\sqrt{2}} \\ & =\frac{\left(\sigma _1-\sigma _2\right) q a}{\sqrt{2} \varepsilon _0} \end{aligned} $$
