Electric field in a spherical capacitor.

In summary, the electric field at the surface of the inner sphere in a spherical capacitor with a constant potential difference is minimum when the radius of the inner sphere is half of the radius of the outer sphere, and the equation for the electric field at the surface can be expressed in terms of a and Δϕ. The guidelines for PF homework require an attempt at a solution to be shown.
  • #1
Felpudio
3
0

Homework Statement



The potential difference Δϕ between the plates of a spherical capacitor is kept constant. Show that then the electric field at the surface of the inner sphere will be a minimum if a=(1/2)b, find that minimum.
Where: a=radius of the inner sphere, b=radius of the outside sphere.

Homework Equations


The potential difference between the plates is [tex]Δϕ=(Q/4πϵ_0)(1/b-1/a)[/tex]
 
Last edited:
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  • #2
Hi Fel, welcome to PF :smile: !

There is something special about the PF homework part you need to know: the guidelines require you present an attempt at solution !

So no point in erasing part 3 of the template: we can't help until you show an effort!

The Attempt at a Solution


For a start, you might bring in an equation for the electric field at the surface of the inner sphere, expressed in a and ##\Delta \phi##.
 

1. What is an electric field in a spherical capacitor?

An electric field in a spherical capacitor is a region of space where an electric charge experiences a force. It is created by the separation of positive and negative charges on the surfaces of the capacitor.

2. How is the electric field strength in a spherical capacitor calculated?

The electric field strength in a spherical capacitor can be calculated using the formula E = Q/(4πε₀r²), where Q is the charge on the capacitor, ε₀ is the permittivity of free space, and r is the distance from the center of the capacitor to the point where the field is being measured.

3. What factors affect the electric field in a spherical capacitor?

The electric field in a spherical capacitor is affected by the charge on the capacitor, the distance between the plates, and the permittivity of the material between the plates. It is also affected by the shape and size of the capacitor.

4. How does the electric field change inside a spherical capacitor?

The electric field inside a spherical capacitor is constant and directed radially from the positive to the negative plate. As the distance from the center increases, the electric field strength decreases.

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

The electric field in a spherical capacitor plays a crucial role in the functioning of electronic devices, as it allows for the storage and transmission of electrical energy. It also helps in understanding the behavior of charged particles in an electric field.

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