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Dear Manik,
The key to solving this question is applying Gauss Law through drawing Gaussian surfaces. The example in your book probably reached the result you give by drawing a cylinder perpendicularly through a charged sheet. If not, see the explanation here under the section "Field of an Infinite Plane Sheet of Charge". You need to understand how exactly this gives you the result E=σ2?0
For this particular geometry, the following Gaussian surfaces should be used:
The red rectangle is the surface you should use to find the field at A. The two green rectangles should be used to find the field at B. And the two blue rectangles should be used to find the field at C. Note that each rectangle in fact represents a cylindrical Gaussian surface.
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options c and D
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