Energy Stored in Parallel Plate Capacitor – Rankers Physics

Parallel Plate Capacitor: Practice Problem & Solution

A parallel plate capacitor has a uniform electric field \(\vec{E}\) in the space between the plates. If the distance between the plates is \(d\) and the area of each plate is \(A\), the energy stored in the capacitor is (\(\varepsilon_0\) = permittivity of free space)
\(\frac{E^2 Ad}{\varepsilon_0}\)
\(\frac{1}{2} \varepsilon_0 E^2\)
\(\varepsilon_0 EAd\)
\(\frac{1}{2} \varepsilon_0 E^2 Ad\)

Solution Explained:

To solve this problem, we apply the core principles of Parallel Plate Capacitor. Understanding the underlying formula is key to arriving at the correct answer below:

The energy density of the electric field is given by \(u = \frac{1}{2}\varepsilon_0 E^2\). Thus, the total energy stored is \(U = u \times \text{Volume} = \frac{1}{2}\varepsilon_0 E^2 Ad\).

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Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. A parallel plate capacitor has plates with area \(A\) and separation \(d\). A battery charges the plates to a potential difference \(V_0\). The battery is then disconnected and a dielectric slab of thickness \(d\) is introduced. The ratio of energy stored in the capacitor before and after slab is introduced, is:
2. The energy and capacity of a charged parallel plate capacitor are $E$ and $C$ respectively. Now a dielectric slab of $\epsilon_{r}=6$ is inserted in it then energy and capacity becomes (Assuming charge on plates remains constant): (1999)
3. Assertion (A): Circuits containing high capacity capacitors, charged to high voltage should be handled with caution, even when the current in the circuit is switched off. Reason (R): When an isolated capacitor is touched by hand or any other part of the human body, there is an easy path to the ground available for the discharge of the capacitor.  
4. Assertion (A): When outer grounded shell of a two charged concentric shell system is removed, the capacitance of system decreases. Reason (R): Electric field will spread in vast region till infinity.  
5. A capacitor is charged by connecting a battery across its plates. It stores energy U. Now the battery is disconnected and another identical capacitor is connected across it, then the energy stored by both capacitors of the system will be