Electromagnetic Waves

Step 1: Understanding displacement current.
Displacement current is a concept introduced by Maxwell and is associated with a time-varying electric field. The displacement current density is given by Thus, displacement current exists only when the electric field changes with time.
Step 2: Examine Region I.
In Region I, This electric field depends on both position and time . Since it contains the term , the electric field varies with time. Therefore, Hence displacement current exists in this region.
Step 3: Examine the remaining regions.
Region II: This is constant and does not vary with time, so Region III: This depends only on position and not on time. Region IV: Again, this depends only on position and not on time. Therefore, in Regions II, III and IV the electric field does not change with time, so no displacement current exists.
Step 4: Conclusion.
Displacement current exists only where the electric field varies with time, which occurs in Region I.
Final Answer: I.