Change in energy stored in a spherical Capacitor

Feb 13, 2023

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?

Feb 13, 2023

kuruman

Science Advisor

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Your solution looks OK. You probably made a calculation error. Please post your substitutions, final answer and the answer you were told is correct.

Mar 18, 2023

ssarpal

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

3. How does the dielectric material affect the energy stored in a spherical capacitor?

The dielectric material between the two plates of a spherical capacitor affects the energy stored by increasing the capacitance. This is because the dielectric material has a higher permittivity than air, allowing for more charge to be stored on the plates, resulting in an increase in energy stored.

5. What factors can cause a change in the energy stored in a spherical capacitor?

The energy stored in a spherical capacitor can be affected by changes in voltage, distance between plates, dielectric material, and plate size. Additionally, changes in the electric field, temperature, and humidity can also impact the energy stored in a spherical capacitor.

Change in energy stored in a spherical Capacitor

Attachments

1. How does the energy stored in a spherical capacitor change with distance?

2. What happens to the energy stored in a spherical capacitor when the voltage is changed?

3. How does the dielectric material affect the energy stored in a spherical capacitor?

4. Is the energy stored in a spherical capacitor affected by the size of the plates?

5. What factors can cause a change in the energy stored in a spherical capacitor?

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