Field Energy and Co-energy in a Linear Electromagnetic Circuit

In a linear electromagnetic circuit, the field energy and co-energy are important concepts that relate to the energy stored in the system. Let's explore each of these terms and understand their relationship.

Field Energy
The field energy refers to the energy stored in the magnetic field (B) and electric field (E) of the circuit. It represents the energy required to establish and maintain these fields. The field energy is given by the equations:

- Magnetic Field Energy: E_magnetic = (1/2) * L * I^2
- Electric Field Energy: E_electric = (1/2) * C * V^2

Where L is the inductance, I is the current, C is the capacitance, and V is the voltage.

Co-energy
The co-energy, also known as the dual of field energy, is the energy stored in the circuit elements due to the interaction with the magnetic and electric fields. It represents the energy released when the fields collapse or change. The co-energy is given by the equations:

- Magnetic Co-energy: W_magnetic = (1/2) * L * I^2
- Electric Co-energy: W_electric = (1/2) * C * V^2

It is important to note that the co-energy is defined in terms of the variables (current or voltage) that are not directly associated with the energy storage element (inductor or capacitor).

Relationship between Field Energy and Co-energy
In a linear electromagnetic circuit, the field energy and co-energy are equal. This means that the energy stored in the fields is equal to the energy stored in the circuit elements due to their interaction with the fields. Mathematically, we can express this relationship as:

- Magnetic Field Energy = Magnetic Co-energy
- Electric Field Energy = Electric Co-energy

Therefore, the correct statement is option 'B': Field energy is equal to the co-energy.

This relationship is a consequence of the principle of energy conservation, which states that energy cannot be created or destroyed but can only be transformed from one form to another. In a linear electromagnetic circuit, the energy transformations occur between the fields and the circuit elements, resulting in the equality between field energy and co-energy.

By understanding the relationship between field energy and co-energy, we can analyze the energy balance in a linear electromagnetic circuit and design efficient systems that minimize energy losses.