Question

Four infinitely large planar charged sheets are placed parallel to each other as shown in Figure 1. Find the magnitude of electric field at point P.

• A. \(\frac{\sigma }{\epsilon _{0}}\)
• B. \(\frac{2\sigma }{\epsilon _{0}}\)
• C. \(\frac{\sigma }{2\epsilon _{0}}\)
• D. \(\frac{3\sigma }{\epsilon _{0}}\)

Hint:

Each infinite sheet gives a uniform field \(\sigma/2\epsilon_0\); add the fields from the four sheets as vectors.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
An infinite sheet of charge density \(\sigma\) produces a uniform field of magnitude \(\dfrac{\sigma}{2\epsilon_0}\), pointing away from a positive sheet and towards a negative one.

Step 2: Superpose the sheets
Point P lies between the third and the fourth sheet. Take the rightward direction as positive. The three sheets on the left together contribute a field to the right, and the fourth sheet on the right pushes towards the left.

Step 3: Result
Adding these contributions vectorially gives a net field of magnitude \(\dfrac{\sigma}{\epsilon_0}\) at P.

Final Answer:
The magnitude of the electric field at P is \(\dfrac{\sigma}{\epsilon_0}\). \[ \boxed{\text{(A) }\dfrac{\sigma }{\epsilon _{0}}} \]