JEE Mains · Physics · STD 12 - Electric charges and fields
- JEE Mains 2020
- Medium
- MCQ
Two infinite planes each with uniform surface charge density \(+\sigma\) are kept in such a way that the angle between them is \(30^{\circ} .\) The electric field in the region shown between them is given by
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(\frac{\sigma}{2 \varepsilon_{0}}\left[\left(1-\frac{\sqrt{3}}{2}\right) \hat{\mathrm{y}}-\frac{\hat{\mathrm{x}}}{2}\right]\)
Step-by-step Solution
Detailed explanation
Electric field due to each sheet is uniform and equal to \(\mathrm{E}=\frac{\sigma}{2 \varepsilon_{0}}\)
Now net electric field between plates
\(\overrightarrow{\mathrm{E}}_{\mathrm{net}} =\mathrm{E} \cos 60^{\circ}(-\hat{\mathrm{x}})+\left(\mathrm{E}-\mathrm{E} \sin 60^{\circ}\right)(\hat{\mathrm{y}})\)
\(=\frac{\sigma}{2 \varepsilon_{0}}\left[-\frac{\hat{\mathrm{x}}}{2}+\left(1-\frac{\sqrt{3}}{2}\right) \hat{\mathrm{y}}\right]\)
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