CBSE Class 12 Physics 2026: question 25

Hints

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Step-by-step solution

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1. Displacement current is the current that arises due to a time-varying electric field (changing electric flux) in a region, e.g. in the gap between capacitor plates, where no charges flow; it produces a magnetic field just like conduction current.

   1 mark

2. While a parallel plate capacitor (plate area A) is charging, let the charge be q at time t. Field between plates: $E=\frac{q}{{\epsilon }_{0}A}$, so electric flux ${\varphi }_E=EA=\frac{q}{{\epsilon }_0}$.

   ½ mark

3. $\frac{d{\varphi }_E}{dt}=\frac{1}{{\epsilon }_0}\frac{dq}{dt}\Rightarrow {\epsilon }_0\frac{d{\varphi }_E}{dt}=\frac{dq}{dt}=i$. This current in the gap (equal to the conduction current in the wires, maintaining continuity) is $i_d={\epsilon }_0\frac{d{\varphi }_E}{dt}$.

   1 mark

4. For a conductor with constant voltage, the electric field (and flux) is constant, so $\frac{d{\varphi }_E}{dt}=0$ and $i_d=0$.

   ½ mark

Answer: i_d = ε₀ dφ_E/dt; i_d = 0 for constant voltage

Revise the chapter

• Chapter: Electromagnetic Waves (notes, formulas, where marks are lost and every past question)
• Topic: Displacement Current