How do you calculate the inductance of a metal sphere with electrical contacts?

In summary, calculating the inductance of a solid sphere can be done by assuming a current flowing through the sphere and then calculating the magnetic field and total magnetic field energy. The total inductive energy can then be equated to the calculated magnetic field energy to find the inductance.
  • #1
John Shillington
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Hey everyone this is my first thread i was wondering how you calculate the inductance of a solid sphere. Say a sphere for example of 5cm diameter with electrical contacts on opposing sides 0.5 cm in diameter.
Any help would be much appreciated
 
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  • #2
The simplest way is to assume a current I flowing through the sphere. Then, given this I, calculate the magnetic field everywhere. Then, calculate the total magnetic field energy by integrating B^2/(2*μ0) over all space. This should give an answer proportional to I^2. The total inductive energy is L*I^2/2, so you can calculate L by equating the total magnetic field energy to the inductive energy L I^2/2.
 
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  • #3
Thanks for your reply, it was informative.
 
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1. What is inductance?

Inductance is a measure of the ability of a conductor to store energy in the form of a magnetic field when an electric current flows through it.

2. How is inductance calculated?

Inductance is calculated by dividing the magnetic flux through a loop by the current passing through the loop. It is measured in units called Henrys (H).

3. What is the inductance of a metal sphere?

The inductance of a metal sphere is dependent on its size, shape, and material properties. It can be calculated using the formula L = (μ0μr * A)/ (2πr), where μ0 is the permeability of free space, μr is the relative permeability of the material, A is the surface area of the sphere, and r is the radius of the sphere.

4. How does the inductance of a metal sphere affect its electrical properties?

The inductance of a metal sphere affects its electrical properties by determining its ability to store energy in the form of a magnetic field. This can impact the behavior of the sphere in an electrical circuit, such as its ability to resist changes in current or voltage.

5. Can the inductance of a metal sphere be changed?

Yes, the inductance of a metal sphere can be changed by altering its size, shape, or material properties. For example, increasing the surface area or using a material with a higher permeability can increase the inductance of the sphere.

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