We know that the total number of magnetic lines which are passing through a given specific region is simply magnetic flux. Therefore, this post will discuss magnetic flux in a magnetic circuit.

**A magnetic field causes a certain amount of magnetic flux to exist. Furthermore, magnetic flux is always in the form of a closed loop. As a result of the presence of a magnetic field, magnetic circuits are now known as such. Therefore, it is also true that magnetic flux exists in magnetic circuits.**

Let’s take the time to fully comprehend magnetic flux in a magnetic circuit.

**Is there a magnetic flux in a magnetic circuit?**

Circuits are closed pathways through which a quantity is passed and are composed of a variety of components. Magnetic circuits are composed of magnetic materials and have closed paths.

**When an electric current travels along a magnetic material’s closed route, the moving charges inside the material create a magnetic field within the magnetic circuit. All of these magnetic field lines that are traveling through the magnetic circuit are simply magnetic flux.**

**Therefore, magnetic circuits can be defined as closed paths composed of magnetic materials that allow magnetic flux to travel through them.**

**What is the magnetic flux in a magnetic circuit?**

In the magnetic circuit, the actual interpretation of magnetic flux does not change.

**If we say that a magnetic field exists in a magnetic circuit, it also indicates the presence of magnetic force. Magnetic flux is a magnetic field measurement. As a result, it is also a helpful tool in describing the effect of magnetic force in that magnetic circuit.**

If we compare an electric circuit to a magnetic circuit, then in an electric circuit, an electric current passes through it. While in a magnetic circuit, magnetic flux passes through it. When a voltage is provided to an electric circuit, the current tends to flow down the path with the least resistance. In the same manner, **magnetic flux follows the route of least reluctance. **

Thus, the magnetic flux in a magnetic circuit serves the same purpose as the electric current in an electric circuit. Alternatively, we may say that **it is analogous to an electric current.**

**How to find the magnetic flux of a magnetic circuit?**

When a magnetic field and an area element are multiplied, the result is the magnetic flux.

In a broader sense, magnetic flux is defined as the scalar product of two vector products:

**The magnetic field B &****The circuit’s area element A.**

**The magnetic flux through any surface of a magnetic circuit is calculated quantitatively using the integral of the magnetic field B over the surface’s area A.**

Thus, we can write:

𝜙_{m}= ∬_{s} B ᐧ dA

Thus, we can write:

𝜙_{m}= BA cos𝜃 ……….(1)

Where,

𝜙_{m} : Magnetic Flux

B : Magnetic field

A : Area element of the magnetic circuit

𝜃 : Angle between magnetic field and area element of magnetic circuit

But when the magnetic field and cross sectional area of the magnetic circuit are perpendicular to each other, then 𝜃 = 90. Thus, magnetic flux is:

𝜙_{m}= BA ……….(2)

Typically, the cross-sectional area of the circuit is selected as the area A for the magnetic circuit to calculate the magnetic flux.

As we know, an electromotive force is responsible for driving the current of the electric charges. **Similarly, the magnetic flux in the magnetic circuits is driven by the magnetomotive force (MMF).** Consider the magnetic circuit whose length is l and has N numbers of wound and current of I ampere passes through it. Thus, mmf is given by:

F_{m} = NI ……….(3)

**Thus, mmf is nothing but the total current linked to that particular magnetic circuit.**

The magnetic field strength for a homogeneous and uniform cross-sectional area magnetic circuit is defined as the mmf per unit length. As a result, magnetic field strength:

H = NI / l ……….(4)

Where, H : Magnetic Field strength

However, the magnetic field in terms of magnetic field strength is given by:

B = 𝜇H ……….(5)

Where, 𝜇 : Magnetic permeability

Thus, putting the value of H in the above equation, we get:

B = 𝜇 NI / l ……….(6)

Using the magnetic field value from equation (6) in the magnetic flux equation (2):

……….(7)

Where,

l/𝜇 A = R (Reluctance)

Equation (7) is the formula to determine the magnetic flux in a magnetic circuit.

**What are the factors that affect magnetic flux in a magnetic circuit?**

The magnetic flux in any magnetic circuit can be affected by four factors, which are listed below:

- Cross sectional area of magnetic circuit A (Eq. 1): The circuit’s cross sectional area and magnetic flux are also directly related. The greater the area of the circuit, the greater the flux that can pass through it.
- The angle between magnetic field B and area element A (Eq. 1): Maximum magnetic flux can be penetrated via the circuit when the magnetic field is perpendicular to the surface.
- Magnetic field strength H (Eq. 5): The magnetic flux in a magnetic circuit and the strength of the magnetic field are both associated. The magnetic flux in a circuit increases when the magnetic field produced in the circuit is strong.
- Current flow through the magnetic circuit I (Eq. 7): Magnetic force and current are inextricably linked. As the current flow increases, the magnetic force increases by raising the strength of the field; hence, flux increases as well.

As mentioned above, a small change in the factor affects the magnetic flux in a magnetic circuit.

**Problem: Given a magnetic system (ring), with a radius of cross-section r =3.5 cm, the number of turns N= 600 and the relative permeability of iron is 900 and current passing through it is 0.15 A. Then calculate magnetic flux in a magnetic circuit.**

**Given:**

Radius of cross-section r = 3.5 cm = 0.035 m

Number of turns N = 600

Relative permeability of iron 𝜇r = 900

Current passing through circuit I = 0.15 A

**Find:**

Magnetic flux 𝜙_{m} =?

**Solution:**

Area of the magnetic ring A = 𝜋r2 = 3.14 × (0.035)2 =3.8 × 10-3 m2

Permeability:

𝜇 = 𝜇0𝜇r = 4𝜋 × 10-7 × 900

Length of the ring:

l = 2𝜋r = 2𝜋 × 0.035 m

Magnetic flux:

𝜙_{m} = 1.75 mWb

**So, in this case, the magnetic flux of a given magnetic circuit is 1.75 mWb.**

#### Summary:

**We learn from this post that magnetic circuits allow magnetic flux to pass through them. Furthermore, the passing magnetic flux describes the effect of the magnetic force generated in the circuit. It is comparable to the electric current flowing through an electric circuit.**