Energy stored in the electric field of a capacitor

In summary: b) correct, putting the capacitors together increases their capacitance.c) incorrect, the put together capacitors have no energy
  • #1
jersey
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0

Homework Statement



The figure shows cross-sectional views of two cubical capacitors, and a cross-sectional view of the same two capacitors put together so that their interiors coincide. A capacitor with the plates close together has a nearly uniform electric field between the plates, and almost zero field outside; these capacitors don’t have their plates very close together compared to the dimensions of the plates, but for the purpose of this problem, assume that they still have approximately the kind of idealized field pattern shown in the figure. Each capacitor has an interior volume of 1.00 m3, and is charged up to the point where its internal field is 1.00 V/m.

Diagram 1
---┴---
↓↓↓↓↓
↓↓↓↓↓
---┬---

Diagram 2
-→→-
-→→-
-→→-
┤→→├
-→→-
-→→-

Diagram 3 (This diagram has the same four sides and is empty on the inside)
---┴---

(a) Calculate the energy stored in the electric field of each capacitor when they are separate.

(b) Calculate the magnitude of the interior field when the two capacitors are put together in the manner shown. Ignore effects arising from the redistribution of each capacitor’s charge under the influence of the other capacitor.

(c) Calculate the energy of the put-together configuration. Does assembling them like this release energy, consume energy, or neither?

Homework Equations



Energy stored, W = ½ QV = ½ CV2 joules
Charge Q = CV where C is the capacitance in Farads

charge Q is measured in coulombs (C)

If the dielectric (the material between the plates) is a vacuum, Capacitance C = e0 (A / l) where A is the area of the capacitor plates, and l is the distance between them.

e0 is the permittivity of free space (8.85X10-12)

If the dielectric is another material, capacitance is given by:

C = e0 (A / l) where er is the relative permittivity, which varies between materials.

Putting capacitors in parallel increases the total capacitance:

C = C1 + C2 + C3 ...


The Attempt at a Solution



a) C=8.85 x 10^-12 x 1/1
=8.85 x 10^-12

W= 1/2cV^2
=1/2 (8.85 x 10^-12) x 1.0^2
=4.425 x 10^-12 J

I'm stuck, am i even on the right track here?
 
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  • #2
you answered a) correctly
 
  • #3
What is the formula for magnitude of the inner field?
 

Related to Energy stored in the electric field of a capacitor

1. What is the definition of energy stored in the electric field of a capacitor?

The energy stored in the electric field of a capacitor is the potential energy that is stored in the capacitor due to the separation of charge between its two plates. This energy is stored in the form of an electric field that is created between the plates of the capacitor.

2. How is the energy stored in a capacitor calculated?

The energy stored in a capacitor can be calculated using the formula E = 1/2 * C * V^2, where E is the energy stored, C is the capacitance of the capacitor, and V is the voltage across the capacitor. This formula shows that the energy stored is directly proportional to the capacitance and the square of the voltage.

3. What factors affect the amount of energy stored in a capacitor?

The amount of energy stored in a capacitor is affected by two main factors: the capacitance and the voltage. A higher capacitance or voltage will result in a higher amount of energy stored. Additionally, the distance between the plates and the type of material used for the plates can also affect the energy stored.

4. How does the energy stored in a capacitor affect its performance?

The energy stored in a capacitor affects its performance by determining how much charge it can hold and how long it can hold that charge. A capacitor with a higher energy storage capacity will be able to hold more charge and discharge it for a longer period of time.

5. Can the energy stored in a capacitor be released?

Yes, the energy stored in a capacitor can be released through a process called discharge. When a circuit is connected to both plates of the capacitor, the stored energy will flow out and power the circuit. This process can be repeated as long as the capacitor is able to hold a charge.

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