Six infinitely large and thin non-conducting sheets are fixed in configurations I and II. As shown in the figure, the sheets carry uniform surface charge densities which are indicated in terms of σ0. The separation between any two consecutive sheets is 1 μm. The various regions between the sheets are denoted as 1, 2, 3, 4 and 5. If σ0=9 μC/m², then which of the following statements is/are correct: (Take permittivity of free space ϵ0=9×10−12 F/m):
(A)In region 4 of the configuration I, the magnitude of the electric field is zero.✓ Correct
(B)In region 3 of the configuration II, the magnitude of the electric field is ϵ0σ0.
(C)Potential difference between the first and the last sheets of the configuration I is 5 V.
(D)Potential difference between the first and the last sheets of the configuration II is zero.
Answer: (A)
Solution
Configuration I: Sheets have alternating charges +σ0,−σ0,+σ0,−σ0,+σ0,−σ0.
In region 4, the net electric field is:
E4=2ϵ0σ0[1−1+1−1−1+1]=0
Potential difference:
Vfirst−Vlast=ϵ03σ0d=9×10−123×9×10−6×10−6=3 V
Configuration II: The field in region 3 is 2ϵ0σ0, not ϵ0σ0. The potential difference is 2ϵ0σ0d=0.
Only option (A) is correct.
JEE Advanced · 2025 · 18 May 2025 · Paper 2 · One or more correct options
