Electrostatics 5 Question 25
27. Three infinitely long charge sheets are placed as shown in figure. The electric field at point $P$ is
(2005, 1M)
(a) $\frac{2 \sigma}{\varepsilon _0} \hat{\mathbf{k}}$
(b) $-\frac{2 \sigma}{\varepsilon _0} \hat{\mathbf{k}}$
(c) $\frac{4 \sigma}{\varepsilon _0} \hat{\mathbf{k}}$
(d) $-\frac{4 \sigma}{\varepsilon _0} \hat{\mathbf{k}}$
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Solution:
- All the three plates will produce electric field at $P$ along negative $z$-axis. Hence,
$$ \mathbf{E} _p=\frac{\sigma}{2 \varepsilon _0}+\frac{2 \sigma}{2 \varepsilon _0}+\frac{\sigma}{2 \varepsilon _0}(-\hat{\mathbf{k}})=-\frac{2 \sigma}{\varepsilon _0} \hat{\mathbf{k}} $$
$\therefore$ Correct answer is (b).
