Electric field between electrodes of half-filled spherical capacitor

In summary, the question asks to find the magnitude of electric field strength between the electrodes of a spherical capacitor with a uniform isotropic dielectric filling half the space between the electrodes. The solution involves using the equation V1 - V2 = -∫E.ds and results in E = q/2∏εo(ε + 1)r2. Additionally, it is mentioned that the situation can also be solved by considering two capacitors in series and by using Gauss's Law.
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Homework Statement



Half the space between two concentric electrodes of a spherical capacitor is filled with uniform isotropic dielectric with permittivity ε. The charge of the capacitor is q. Find the magnitude of electric field strength between the electrodes as a function of distance r from center of electrode.

Answer → E = q/2∏εo(ε + 1)r2

Homework Equations



V1 - V2 = -∫E.ds

The Attempt at a Solution



I tried to find the potential diference between electrod using above equation but its not working
 
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Related to Electric field between electrodes of half-filled spherical capacitor

1. What is a half-filled spherical capacitor?

A half-filled spherical capacitor is a type of capacitor that consists of two concentric, spherical electrodes with a dielectric material in between. It is called "half-filled" because the space between the two electrodes is only partially filled with the dielectric material.

2. How is the electric field between the electrodes of a half-filled spherical capacitor calculated?

The electric field between the electrodes of a half-filled spherical capacitor can be calculated using the formula E = Q/(2πεr³), where Q is the charge on the electrodes, ε is the permittivity of the dielectric material, and r is the distance between the electrodes.

3. What factors affect the strength of the electric field in a half-filled spherical capacitor?

The strength of the electric field in a half-filled spherical capacitor is affected by the distance between the electrodes, the charge on the electrodes, and the permittivity of the dielectric material. It is also influenced by the shape and size of the electrodes.

4. How does the electric field change as the capacitor is being filled?

As the capacitor is being filled, the electric field between the electrodes decreases. This is because the dielectric material reduces the voltage between the electrodes, resulting in a decrease in the electric field. However, the electric field can still be calculated using the same formula mentioned above.

5. What is the significance of the electric field in a half-filled spherical capacitor?

The electric field in a half-filled spherical capacitor is important because it determines the capacitance and energy storage capacity of the capacitor. It also plays a crucial role in the functioning of electronic devices that use capacitors, such as radios, televisions, and computers.

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