If the distance between the plates of a parallel plate capacitor is increased by maintain the constant charge on the capacitor, then the energy density between the plates will:

CONCEPT:

Capacitor:

• The capacitor is a device in which electrical energy can be stored.
  • In a capacitor two conducting plates are connected parallel to each other and carrying charges of equal magnitudes and opposite sign and separated by an insulating medium.
  • The space between the two plates can either be a vacuum or an electric insulator such as glass, paper, air, or semi-conductor called a dielectric.​

​Parallel plate capacitor:

• A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance.
  • The space between the two plates can either be a vacuum or an electric insulator such as glass, paper, air, or semi-conductor called a dielectric.​

The energy stored in the capacitor is given as,

\(⇒ U=\frac{1}{2}QV=\frac{1}{2}CV^2=\frac{Q^2}{2C}\)

Energy density:

• It is defined as the energy stored per unit volume of space between the plates.
• Energy density u between the plates is given as,

\(⇒ u =\frac{1}{2}\epsilon_oE^2\)

Where C = capacitance of the capacitor, Q = charge on the plates, V = potential difference between the plates, and E = electric field intensity between the plates

EXPLANATION:

• Energy density u between the plates is given as,

\(⇒ u =\frac{1}{2}\epsilon_oE^2\)

• From the above equation, it is clear that the energy density of the parallel plate capacitors does not depend upon the distance between the plates of a parallel plate capacitor.
• Therefore, if the distance between the plates of a parallel plate capacitor is increased by maintaining the constant charge on the capacitor, then the energy density between the plates will remain the same. Hence, option 3 is correct.