How to Calculate Electric Energy in a Spherical Capacitor with Dielectric?

[Nivlac2425]

Homework Statement

I am doing a problem in my physics textbook where there is two concentric hollow spheres and the space between them is filled with a dielectric substance. The question asks for the electric energy in this space.

Homework Equations

The only given equation for the C of parallel plate capacitors in my textbook is C = A(epsilon)(dielectric constant)/d There is nothing for spherical capacitors
Since the problem has two concentric circles, the plate areas are different. I am not sure if this is still the correct formula to use in this case.

The Attempt at a Solution

Since the change in voltage is given in the text, I need to calculate the capacitance of the 'capacitor' to find the contained electrical energy. The areas are different, so the equation above for C might not apply. How should I proceed from here?

Thank you for helping out! =)

EDIT: I'm sorry, I've figured this out already! I used the energy density of the space, which is the energy(electric energy here) over the volume of the space. Energy density is also equal to 1/2 (dielectric const.)(epsilon)(electric field)^2 so I worked my way to the electrical energy.
Thanks anyway!

 

[anathema]

Hi there,

It's great that you were able to figure out the solution on your own! it is important to approach problems with critical thinking and problem-solving skills, which you have clearly demonstrated.

Just to add to your solution, you are correct in using the energy density equation to calculate the electric energy in the space between the two concentric spheres. This is because the electric field in this space is not uniform, and therefore the formula for parallel plate capacitors may not apply.

Another way to approach this problem is to use the formula for the capacitance of a spherical capacitor, which is C = 4(pi)(epsilon)(r1)(r2)/(r2-r1). In this case, r1 and r2 refer to the radii of the inner and outer spheres, respectively. You can then use this capacitance value in the formula for electric energy, which is E = 1/2 QV, where Q is the charge on the capacitor and V is the voltage across the capacitor.

I hope this helps and keep up the good work in your studies!

 

[thomate1]

I would suggest that you first confirm the given equation for the capacitance of parallel plate capacitors in your textbook. You can do this by researching other reliable sources or consulting with your professor or a fellow scientist. Once you have confirmed the equation, you can proceed to apply it in your problem, taking into account the different plate areas. If the equation does not apply, you can try to find other equations or methods that are more suitable for the given scenario. It is important to carefully consider the properties and geometry of the problem before choosing an appropriate equation or method. Additionally, it would be helpful to show your calculations and steps in arriving at your solution, as this will help you and others understand and verify your answer.