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Two thin dielectric slabs of dielectric constants K1K_1 and K2K_2 (K1<K2K_1 < K_2) are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field EE between the plates with distance dd as measured from the plate P is correctly shown by:

A

Option 1

B

Option 2

C

Option 3

D

Option 4

Step-by-Step Solution

The electric field between the plates of a capacitor in vacuum (or air) is E0E_0. When a dielectric slab of dielectric constant KK is introduced, the electric field inside the dielectric decreases to E=E0KE = \frac{E_0}{K} [NCERT Class 12, Sec 2.10].

  1. Inverse Relationship: The electric field is inversely proportional to the dielectric constant (E1/KE \propto 1/K).
  2. Comparison: We are given K1<K2K_1 < K_2. Therefore, 1K1>1K2\frac{1}{K_1} > \frac{1}{K_2}.
  3. Field Magnitude: This implies that the electric field inside the first slab (E1=E0/K1E_1 = E_0/K_1) is greater than the electric field inside the second slab (E2=E0/K2E_2 = E_0/K_2).
  4. Graph Analysis: The correct graph should show regions of constant electric field. The field will be highest in the air regions (E0E_0), intermediate in the slab with K1K_1, and lowest in the slab with K2K_2. Thus, the graph steps down from E0E_0 to E1E_1, goes back to E0E_0 (if there is an air gap), and then steps down to a lower value E2E_2 for the second slab.
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