What Is the Correct Calculation of Energy Density in a Charged Capacitor?

AI Thread Summary
A parallel-plate capacitor with a capacitance of 16 μF stores 1.7 J of energy and has a plate separation of 0.35 mm. To calculate energy density, the volume between the plates must be determined using the formula for capacitance, C = (ε₀ * A) / d, where A is the area of the plates. The volume is calculated as A multiplied by d, and energy density is found by dividing the stored energy by this volume. The discussion highlights the need to find the area to compute the volume accurately for the energy density calculation.
baker265
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Homework Statement



A parallel-plate capacitor with C = 16 mu or micro FF is charged so as to contain 1.7 J of energy. If the capacitor has a vacuum between plates that are spaced by 0.35 mm, what is the energy density (the energy per unit volume)?

I am a little lost of this problem and have no idea if I'm doing it correctly. Am I ?

Homework Equations


v = A*d
E,density=U/v


The Attempt at a Solution


v=16e-3/.35e-3=45.71
E=1.7/45.71=.0371 J/m^3
 
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baker265 said:

Homework Statement



A parallel-plate capacitor with C = 16 mu or micro FF is charged so as to contain 1.7 J of energy. If the capacitor has a vacuum between plates that are spaced by 0.35 mm, what is the energy density (the energy per unit volume)?

I am a little lost of this problem and have no idea if I'm doing it correctly. Am I ?

Homework Equations


v = A*d
E,density=U/v


The Attempt at a Solution


v=16e-3/.35e-3=45.71 ?
E=1.7/45.71=.0371 J/m^3

Is the capacitance 16 μF (microfarad)?

How do you calculate the volume?

ehild
 
Yes, I believe that is (microfarad); it doesn't say specifically.
I was very unsure on that step and wasn't quite sure how to compute the volume. Do I even to find the volume?
 
As yo have written, energy density is energy divided by volume. So you need it.

ehild
 
Okay so how do I find the area in order to find volume.
 
What is the formula for the capacitance? ehild
 
C=(k* epsilon_0*A)/d
 
The volume between the plates is given by Ad where 'A' is area of the plates and 'd' is separation between them . 'd' is given whereas 'A' is unknown .

Using C= ε0A/d ,find the value of A.

Now,energy density = Energy stored/volume .
 
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