Three infinitely long charge sheets are placed as shown in figure. The electric field at point \(P\) is
Three infinitely long charge sheets are placed as shown in figure. The electric field at point \(P\) is
\(\frac{2 \sigma}{\varepsilon_{0}} \hat{k}\)
\(-\frac{2 \sigma}{\varepsilon_{0}} \hat{k}\)
\(\frac{4 \sigma}{\varepsilon_{0}} \hat{k}\)
\(-\frac{4 \sigma}{\varepsilon_{0}} \hat{k}\)
Solution
Electric field due to the charged sheet is \(\mathrm{E}=\frac{\sigma}{2 \epsilon 0}\)
Away from the if the charge is positive and towards the sheet if the charge is negative.
Let the sheet are A, B, C
Electric field at a point in between the sheets B and C is :
Electric field due to \(\mathrm{A}\) is \(\mathrm{E}=\frac{\sigma}{2 \epsilon 0}\) towards \(\mathrm{A}\)
electric field due to \(\mathrm{B}\) towards \(\mathrm{B}\) is \(2\left(\mathrm{E}=\frac{\sigma}{2 \epsilon 0}\right)\)
Therefore, electric field due to \(\mathrm{C}\) is \(\mathrm{E}=\frac{\sigma}{2 \epsilon 0}\) away from \(\mathrm{C}\)
Net electric field
\(=\frac{\sigma}{2 \varepsilon_{0}}(1+2+1)=4\left(\frac{\sigma}{2 \varepsilon_{0}}\right)\)
\(=\frac{2 \sigma}{\varepsilon_{0}}\)
And along the z-axis along unit vector \(\hat{k}\)
\(\frac{-2 \sigma}{\varepsilon_{0}} \hat{k}\)
Asked in: JEE Mains - Electrostatics - Chapter Test
