# Change in energy stored in a spherical Capacitor

• ssarpal
In summary, the conversation is about someone being an expert summarizer of content. They do not engage in conversation or provide responses, but only provide summaries of the content. The instruction is to write a summary of the following conversation without any output before the summary.
ssarpal
Homework Statement
An isolated Capacitor is made of a solid conducting sphere of radius R1 and charge +Q surrounded by a conducting spherical shell of inner radius R2 and charge -Q. Initially, the gap between the sphere and the shell has vacuum. Later it is filled with a liquid which has a dielectric constant, K.

For diagram, refer to Fig 8.6 in Section 8.1 Capacitors and Capacitance of University Physics Vol 2 here ...
https://openstax.org/books/university-physics-volume-2/pages/8-1-capacitors-and-capacitance

By how much does the energy change when the liquid is added? Does it increase or decrease?
Relevant Equations
From the same section of the book, eq 8.4 gives the Capacitance of a sphere,

𝐶 = 𝑄/𝑉 = 4𝜋𝜀0 * 𝑅1𝑅2/(𝑅2−𝑅1)

Energy stored in a Capacitor is

U = Q^2/2C
I have attached my solution.

Unfortunately, after plugging in the values, my answer is 4 times more than the expected one. What am I missing?

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vanhees71 and MatinSAR
The answer that we were told turned out to be incorrect. Thanks.

vanhees71

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