A. A parallel-plate capacitor has area A and plate separation d, and it is charg

Question

A. A parallel-plate capacitor has area A and plate separation d, and it is charged to voltage V. Use the formulas from the problem introduction to obtain the formula for the energy U of the capacitor. Express your answer in terms of A, d, V, and appropriate constants.

B. A parallel-plate capacitor has area A and plate separation d, and it is charged so that the electric field inside is E. Use the formulas from the problem introduction to find the energy U of the capacitor. Express your answer in terms of A, d, E, and appropriate constants.

C. Find the energy density u of the electric field in a parallel-plate capacitor. The magnitude of the electric field inside the capacitor is E. Express your answer in terms of E and appropriate constants.

Explanation / Answer

Remember and apply for parallel plate caapcitor, these as formulas

1. Capacitance C = K eoA/d   

where K is dieelctric constant ( for air K = 1)

eo is permnittivity constant = 8.85 e-12

A is area = pi^2 ( for circular plates) and l* b for rectanular plates

and

d is the distance between the plates

2.Charge Q = CV where V is potrntial difference

3. energy stored U = 0.5 QV or 0.5 CV^2 or 0.5 Q^2/C

4. electric field between the plates is E = Q/eo A ( also given by E = V/d)

so here we now apply

5. eenrgy Density u = eenrgy/volume

so

u = E/V = 0.5 eo E^2

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