An empty capacitor is capable of storing 1.0 * 10-4 J of energy when connected to a certain battery. If the distance between the plates is halved and then filled with a dielectric (κ = 4.3), how much energy could this modified capacitor store when connected to the same battery?

Energy stored in a capacitor

= 1/2 C₁V²

capacity of a capacitor

c = εK A / d

k is dielectric and d is distance between plates.

When the distance between the plates is halved and then filled with a dielectric (κ = 4.3)

capacity becomes 4.3 x 2 times

New capacity

C₂ = 8.6 C₁

Energy of modified capacitor

1/2 C₂ V² = 1/2 x 8.6 c x V²

Energy becomes

8.6 times.

Energy stored = 8.6 x 10⁻⁴ J