Q195 / 200 · Manipal (MET) 2014 · Physics

Three infinitely charged sheets are kept parallel to $x-y$ plane having charge densities as shown. Then, the value of electric field at ' $P$ ' is

A
$\frac{-4 \sigma}{\varepsilon_0} \hat{\mathbf{k}}$
B
$\frac{4 \sigma}{\varepsilon_0} \hat{\mathbf{k}}$
Correct answer
C
$\frac{-2 \sigma}{\varepsilon_0} \hat{\mathrm{k}}$
D
$\frac{2 \sigma}{\varepsilon_0} \hat{k}$

Solution

$\begin{aligned} \mathbf{E}_p & =\frac{\sigma}{2 \varepsilon_0}(-\hat{\mathbf{k}})+\frac{(-2 \sigma)}{2 \varepsilon_0}(\hat{\mathbf{k}})+\frac{(-\sigma)}{2 \varepsilon_0}(\hat{\mathbf{k}}) \\ & =\frac{-2 \sigma}{\varepsilon_0} \hat{\mathbf{k}}\end{aligned}$

Hence, the correct answer is option: 'C'.

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