Question

A 5.20 μF, parallel-plate, air capacitor has a plate separation of 4.80 mm and is charged to a potential difference of 500.0 V. Calculate the energy density in the region between the plates. Express your answer in joules per meter cubed. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Electric-field energy.

Answer 1

The energy density in the region between the plates of the parallel-plate capacitor is 60.6 J/m³.E = 60.6 J/m³

Step-by-step explanation:

To calculate the energy density in the region between the plates of a parallel-plate capacitor, we can use the formula:

E = Uc / Ad

where E is the energy density, Uc is the energy stored in the capacitor, and Ad is the volume between the plates.

The energy stored in the capacitor can be calculated using the formula:

Uc = Q² / (2C)

where Q is the charge on the capacitor and C is the capacitance.

Using the given values, we can calculate the energy density as follows:

E = (Q² / (2C)) / Ad

Substituting the values, we have:

E = (500.0 V)² / (2 * 5.20 × 10^-6 F * (4.80 × 10^-3 m))

E = 60.6 J/m³