Spherical capacitor and electric fields

In summary, a spherical capacitor is a type of capacitor that stores electrical energy by creating an electric field between two conductive spherical plates separated by a dielectric material. It works by applying a voltage difference across the plates, resulting in one plate becoming positively charged and the other negatively charged. The capacitance of a spherical capacitor can be calculated using the formula C = 4πε<sub>0</sub>r, where r is the radius of the plates. The electric field inside a spherical capacitor varies inversely with distance from the center, with its strongest point near the plates. Spherical capacitors have practical applications in electronic circuits, power supplies, energy storage, and scientific research.
  • #1
stompyourface
3
0
A spherical capacitor contains:
Region1: solid spherical conductor (radius=0.5mm, Q=7.4 micro coulombs)
Region2: surrounded by a dielectric material (er=1.8, radius extends to 1.2mm,
Region3: outer spherical non-conducting shell (variable charge per unit volume p = 5r, outer radius=2.0 mm)
Determine the electric field everywhere?

Homework Equations





Region 1: [1 r>r1] E = 0
Region 2: [r1 < r < r2] E = 7.4*10^-6 / (4 *∏ *1.8 * ε *r^2) = 3.71*10^4/r^2
Region 3: [r2 < r < r3] Q(r) = 5 ∏ (r4 − r40) = 2.19*10^-10 .
E = ( 7.4*10^-6 + 2.19*10^-10) / (4 ∏ εo) = 6.64*10^4
Total Electric Field = 3.71*10^4/r^2 + 6.64*10^4/r^2
Does this look right
 
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  • #2
?

I would like to provide some clarification and additional information regarding the electric field in this setup.

Firstly, the electric field is a vector quantity, meaning it has both magnitude and direction. In this setup, the electric field will be directed radially outward from the positively charged region (Region 1) towards the negatively charged region (Region 3). This means that the electric field in Region 2 will also be directed radially outward.

Secondly, the electric field in Region 1 and Region 3 can be calculated using the equation E = Q/(4∏εr^2), where Q is the charge and r is the distance from the center of the spherical capacitor. In Region 1, the electric field will be zero since there is no charge present. In Region 3, the electric field will vary depending on the distance from the center of the outer spherical shell.

Thirdly, the electric field in Region 2, where the dielectric material is present, can be calculated using the equation E = Q/(4∏εr^2), where Q is the net charge (taking into account the charge in Region 1 and Region 3) and r is the distance from the center of the spherical capacitor. The dielectric material will affect the electric field by reducing its magnitude according to the dielectric constant (er) of the material.

Finally, in order to determine the electric field everywhere, one would need to take into account the contribution of each region. This can be done by summing up the electric fields from each region using vector addition. The resulting electric field will be the total electric field at any given point in space.

In summary, the electric field in this setup is a combination of the electric fields from each region, taking into account the direction and magnitude of each field. I hope this helps to clarify and provide a more comprehensive understanding of the electric field in this spherical capacitor setup.
 

1. What is a spherical capacitor?

A spherical capacitor is a type of capacitor that has two conductive spherical plates separated by a dielectric material. It is used to store electrical energy by creating an electric field between the two plates.

2. How does a spherical capacitor work?

A spherical capacitor works by storing electrical energy in the form of an electric field between its two conductive plates. When a voltage difference is applied across the plates, one plate becomes positively charged while the other becomes negatively charged. This creates an electric field between the plates that can store energy.

3. What is the formula for calculating the capacitance of a spherical capacitor?

The formula for calculating the capacitance of a spherical capacitor is C = 4πε0r, where C is the capacitance, ε0 is the permittivity of free space, and r is the radius of the capacitor plates.

4. How does the electric field inside a spherical capacitor vary with distance?

The electric field inside a spherical capacitor varies inversely with the distance from the center of the capacitor. This means that the electric field is strongest near the plates and decreases as you move further away from them.

5. What are some applications of spherical capacitors?

Spherical capacitors have various practical applications, including in electronic circuits, power supplies, and energy storage systems. They are also used in scientific research for studying electric fields and in medical devices for delivering targeted electrical stimulation.

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