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Question

Physics Question on Gauss Law

Three infinitely long charge sheets are placed as shown in figure. The electric field at point P is

A

2σε0k^\frac{2\sigma}{\varepsilon_{0}} \hat{k}

B

−2σε0k^- \frac{2\sigma}{\varepsilon_{0}} \hat{k}

C

4σε0k^\frac{4\sigma}{\varepsilon_{0}} \hat{k}

D

−4σε0k^-\frac{4\sigma}{\varepsilon_{0}} \hat{k}

Answer

−2σε0k^- \frac{2\sigma}{\varepsilon_{0}} \hat{k}

Explanation

Solution

The electric field due to an infinite plane sheet of charge is independent of distance of point from the sheet. Applying the principle of superposition of electric field, the total electric field at P due to various plane sheets of charge will be E⃗p=σ2ε0(−k^)+2σ2ε0(−k^)+σ2ε0(−k^)=−2σε0k^\vec{E}_{p}=\frac{\sigma}{2\varepsilon _{0} }\left(-\hat{k}\right)+\frac{2 \sigma }{2\varepsilon_{0}}\left(-\hat{k}\right)+\frac{\sigma }{2\varepsilon_{0}}\left(-\hat{k}\right)=-\frac{2\sigma }{\varepsilon_{0}}\hat{k}