How Are Capacitance and Inductance Inversely Related in Electromagnetism?

[Oscar6330]

Homework Statement

I learned this relationship of Capacitance and Inductance. But I am not able to understand the theory behind the equation or the derivation.

Homework Equations

The equation is [L]=$$\mu \epsilon$$ [C]^-1

The Attempt at a Solution

Can you explain me the theory behind this relation. A small derivation or link will be great

 

[Oscar6330]

there is a not under [meu] as well

 

[nlightner]

The relationship between capacitance and inductance is a fundamental concept in the field of electromagnetism. It is described by the equation [L]=\mu \epsilon [C]^-1, where [L] represents inductance, [C] represents capacitance, \mu is the permeability of the material, and \epsilon is the permittivity of the material.

To understand this relationship, it is important to first understand what capacitance and inductance are. Capacitance is a measure of an object's ability to store electrical charge, while inductance is a measure of an object's ability to store magnetic energy. Both of these properties are related to the material's ability to resist changes in electric and magnetic fields.

The equation [L]=\mu \epsilon [C]^-1 shows that inductance and capacitance are inversely proportional to each other. This means that as one increases, the other decreases. This relationship can be explained by considering how an electric current flows through a circuit.

When an electric current flows through a circuit, it creates a magnetic field around the wire. This magnetic field induces an electric field in the surrounding space, which in turn creates a capacitance between the wires. This capacitance acts as a barrier to the electric current, causing it to flow less easily.

On the other hand, when a changing magnetic field is applied to a circuit, it induces an electric current. This changing current creates an inductance in the circuit, which resists the change in current flow.

Therefore, the relationship between capacitance and inductance can be understood as a balance between the two properties. As one increases, the other decreases, creating a balance that allows for the smooth flow of electric current in a circuit.

As for a derivation or further explanation of this relationship, I would recommend looking into Maxwell's equations, specifically the equations for electric and magnetic fields. These equations form the basis for understanding the relationship between capacitance and inductance. Additionally, there are many online resources and textbooks available that can provide a more detailed explanation of this concept.