Magnetic Circuit: Magnetic Flux, Mmf, Reluctance, other Comparison

Introduction to Magnetic Circuits

We all know that magnets can pull things like pins or nails. But have you ever wondered how this invisible pull works inside machines like fans, motors, or transformers?

Well, it’s all about something called a magnetic circuit.

Just like electric current flows in a loop through wires in an electric circuit, magnetic force or magnetic flux also flows in a loop. This loop is called a magnetic path or magnetic circuit. These loops go around and sometimes through special materials like iron or steel, which help carry the magnetic field more easily.

Magnetic circuits are very important. They are found in many electrical machines such as electric motors, generators, relays, and transformers. These machines cannot work properly unless their magnetic field is strong, smooth, and controlled.

That’s why we must design magnetic circuits carefully. If the path is too weak or too long, the magnetic flux won’t flow properly. But if it’s just right, the machine will work perfectly — saving energy, increasing performance, and reducing heat.

In this chapter, we will learn:

• What magnetic circuits are
• How magnetic lines of force behave
• What materials help carry magnetic flux easily
• How to calculate and improve magnetic circuits
• And why they are important in real-world machines

By the end, you’ll understand the basic principles of magnetism, how a closed magnetic path works, and how these invisible loops of force power so many things in our daily lives.

Magnetic Circuit

🔄 What is a Magnetic Circuit?

A magnetic circuit is just like a path made for a magnet. When we allow magnetic flux (the invisible lines of magnetic force) to move in a round path and come back to where it started, that full loop is called a magnetic circuit.

Imagine a race track where tiny invisible magnetic lines are running in a circle—that’s your magnetic circuit!

🧲 How Does a Magnetic Circuit Work?

In a magnetic circuit, the magnetic flux starts from the north pole (N-pole), goes all the way through a special material like iron or soft steel, and returns to the south pole (S-pole) or the starting point. This path is called the magnetic path.

The materials used in the circuit are called magnetic materials. These materials have high permeability, which means they let magnetic flux pass through very easily—just like how water flows easily through a clean pipe.

🔌 How is Magnetic Flux Created?

To create magnetic flux, we simply wrap a coil of wire around a magnetic material (like an iron core). This coil has many turns, called N turns. When we pass electric current (I) through the wire, the coil becomes an electromagnet.

This electric current produces a force called magnetomotive force (MMF). It pushes the magnetic flux around the iron core, making it follow a closed loop, just like water flowing in a circular pipe.

🧭 An Example You Can Imagine

Let’s take an iron ring and wind a wire around it many times. Now connect the wire to a battery. The moment current flows, magnetic flux (Φ) is created inside the ring. It moves around the ring in a circle and comes back to where it started. This loop is your magnetic circuit.

So if the magnetic path is ABCDA, then the flux flows through ABCDA and completes the circle.

🔍 Key Things to Remember

• A magnetic circuit is the full path followed by magnetic flux.
• The flux starts from the N-pole and comes back to the same place.
• Materials like iron and soft steel are used because they help the flux flow easily.
• Magnetic flux is produced using electric current in a coil—this creates an electromagnet.
• The strength and direction of magnetic flux can be controlled by adjusting the current.

💡 Important Words (Easy Definitions)

• Magnetic Flux (Φ) – Invisible lines of magnetic force.
• Magnetic Field – The area where magnetic force is felt.
• Magnetic Material – Material that lets flux pass easily (e.g. iron).
• Permeability – How easily a material allows magnetic lines to flow.
• Magnetomotive Force (MMF) – The pushing force made by electric current to move magnetic flux.
• Reluctance – The resistance a material gives to magnetic flux. Less reluctance = better magnetic flow.
• Iron Core – The center piece of iron where flux flows.
• Electromagnet – A magnet made by electricity.
  

What is Magnetic Flux and Magnetomotive Force? (Explained Simply)

Let’s understand something amazing about magnetism in a very simple way.

Imagine you have a coil of wire and you pass electric current through it. What happens? A magnetic field is created around it. Now, this magnetic field flows through something called a magnetic core. The amount of magnetic field flowing through the core is called magnetic flux.

🔄 What Affects Magnetic Flux?

The magnetic flux depends on two main things:

1. Current (I) – The more electric current you give, the stronger the magnetic field becomes.
2. Number of Turns (N) – If you increase the number of turns in the coil, the magnetic flux also increases.

So, if you increase the current or the number of turns, you get more magnetic flux. If you reduce them, the flux also reduces.

Now here’s something important…

💡 What is Magnetomotive Force (MMF)?

The product of the number of turns (N) and the current (I) is called the magnetomotive force, or MMF.

It is written as:

MMF = N × I (ampere-turns)

You can think of magnetomotive force as the pushing power that sends magnetic flux through a magnetic circuit, just like electromotive force (EMF) pushes electric current through a wire.

🚧 What is Reluctance in a Magnetic Circuit?

Now let’s talk about something called reluctance. Just like wires resist the flow of electric current, a magnetic circuit resists the flow of magnetic flux. This resistance is called reluctance.

📏 What Reluctance Depends On:

• The length of the magnetic path (a longer path gives more reluctance)
• The cross-sectional area (a bigger area gives less reluctance)
• The material used (some materials allow magnetic flux to pass easily, while others don’t)

So, the better the material and the shorter and thicker the path, the lower the reluctance will be, and more magnetic flux will flow.

🎯 Quick Recap

• Magnetic flux increases with more current and more turns.
• Magnetomotive force (MMF) is the total magnetic “push” given by the coil: MMF = N × I (ampere-turns).
• Reluctance is how much the magnetic circuit resists the magnetic flux.
• Good material and design = Less reluctance = Stronger magnetic field.

Analysis of Magnetic Circuit

Let’s understand how a magnetic circuit works in a very easy way—just like how we learn electric circuits, but here, we deal with magnetism instead of electricity.

🧲 What is a Magnetic Circuit?

A magnetic circuit is a path made mostly of magnetic materials (like iron), through which magnetic flux (ϕ) flows. Just like electric current flows in an electric circuit, magnetic flux flows in a magnetic circuit.

Imagine a soft iron ring or a rectangular core. When we wrap a coil of wire around it and pass electric current through it, it produces magnetic flux. The core helps the magnetic flux to move in a closed path. This full path of magnetic flux is called the magnetic circuit.

📐 Important Parts of a Magnetic Circuit

Let’s take a simple magnetic circuit in the shape of a rectangle (say, A-B-C-D-A). This will help us understand it easily.

• Mean length of the magnetic path = l meters
• Cross-sectional area of the core = a square meters (m²)
• Relative permeability of core material = µr (This tells us how easily the material allows magnetic lines to pass through)
• Current flowing in the coil = I amperes
• Number of turns in the coil = N

When the current passes through the coil, it creates a magnetic field. This magnetic field produces magnetic flux (ϕ) in the core.

📘 Magnetic Flux, Flux Density, and Magnetising Force

Let’s understand three important terms:

• Magnetic Flux (ϕ): It is the total magnetic lines of force produced in the core.
  
• Flux Density (B): It tells us how much magnetic flux is present in a given area.
  
  Formula: B=ϕ/a
  
• Magnetizing Force (H): It shows how strong the magnetic field is per unit length.
  
  Formula: H=N×I/l (Ampere-turns per meter)

🧮 Magnetic Ohm’s Law

In an electric circuit, we know:

Current (I)=Voltage (V)/Resistance (R)

In a magnetic circuit, something very similar happens:

Magnetic Flux (ϕ)=Magnetomotive Force (NI)/Reluctance (ℜ)

Where:

• Magnetomotive Force (m.m.f.) = N × I (measured in Ampere-turns)
• Reluctance (ℜ) = Opposition to magnetic flux, like resistance in electric circuits.
  Formula:

Reluctance=l/µ0​×µr×a

Putting it all together:

ϕ=​N×I/l/µ0​×µr×a = µ0​µraNI​/ l

Important Terms in Magnetic Circuits – Explained Simply

When we study magnetic circuits, there are a few important terms that help us understand how magnetism works in wires, coils, and machines. Let’s explore them in the simplest way possible.

✅ 1. Magnetomotive Force (MMF)

What is it?
Magnetomotive force, also called MMF, is like a “push” that helps magnetic flux move through a magnetic circuit. Just like a battery pushes electric current in a wire, MMF pushes magnetic flux in a magnetic path.

In simple words:
MMF is the force that creates a magnetic field inside a magnetic material.

Formula:
MMF = N × I
Where:

• N = number of turns of the coil
• I = current flowing in amperes

So, the unit of MMF is ampere-turns (AT).

🧲 Real-Life Example:
Imagine you have a coil of wire wrapped around an iron ring. When you pass current through the coil, the MMF pushes magnetic flux around the ring.

✅ 2. Reluctance

What is it?
Reluctance is the opposition to magnetic flux in a magnetic circuit. It tells us how hard or easy it is for magnetic lines to pass through a material.

In simple words:
Reluctance is the enemy of magnetic flux. If reluctance is high, it’s hard for the magnetic field to move. If reluctance is low, the field moves easily.

Formula:
Reluctance (S) = l / (μ × a)
Where:

• l = length of the magnetic path
• a = cross-sectional area
• μ = permeability of the material

Unit: Ampere-turns per weber (AT/Wb)

🧲 Important Tip:

• Magnetic materials like iron or steel have low reluctance – flux flows easily.
• Non-magnetic materials like air, wood, or plastic have high reluctance – flux flows with difficulty.

🧠 Think of it like this:
Reluctance in a magnetic circuit is just like resistance in an electric circuit.

✅ 3. Permeance

What is it?
Permeance is the friend of magnetic flux. It tells us how easily magnetic flux can pass through a material.

In simple words:
Permeance is the opposite of reluctance. If reluctance stops the magnetic flux, permeance allows it to go smoothly.

Formula:
Permeance = 1 / Reluctance
Or,
Permeance = μ × a / l

Unit: Weber per ampere-turn (Wb/AT)

🧲 Remember:

• High permeance means the material is good at carrying magnetic flux.
• Low permeance means the material is not good for magnetic circuits.

🔁 Quick Comparison Table

Comparison Between Magnetic and Electric Circuits

Magnetic circuits and electric circuits may look different, but they have many things in common. Both deal with the flow of something — magnetic flux in one and electric current in the other.

Let’s understand their similarities and differences in a very simple way, using a clear comparison that even a child can understand.

✅ Similarities Between Magnetic and Electric Circuits

These points show that the basic concepts in both circuits follow similar logic, just with different names and units.

❌ Differences Between Magnetic and Electric Circuits

🧠 Final Thoughts

Both magnetic circuits and electric circuits help us understand how energy works in different ways. They are similar in structure, but different in behavior.

• Magnetic circuits deal with magnetic fields and flux.
• Electric circuits deal with electric charge and current.

Knowing their differences and similarities makes it easier to study transformers, motors, generators, and many electrical machines used in real life.

Calculation of Ampere-Turns

Let’s understand how ampere-turns (AT) are calculated in a magnetic circuit, in a way that even a child can understand.

🌟 What is Ampere-Turns?

Ampere-turns means the magnetizing force needed to create magnetic flux in a magnetic circuit. Just like we need effort to push water through a pipe, we need effort (in terms of current and coil turns) to push magnetic flux through a magnetic material.

This effort is called Magnetomotive Force (MMF) and it is measured in ampere-turns (AT).

🧲 What is Magnetic Flux?

Magnetic flux (𝜙) is the total number of magnetic lines passing through a given area in a magnetic circuit. It tells us how much magnetic field is flowing.

✅ Basic Formula of Magnetic Flux

ϕ=MMF/Reluctance

Where:

• 𝜙 = Magnetic Flux (in Weber)
• MMF = Magnetomotive Force (in Ampere-Turns)
• Reluctance = Opposition to the magnetic path (like resistance in electric circuits)

⚡ Ampere-Turns (AT) Formula

To find how many ampere-turns are needed, use the formula:

AT=H×l

Where:

• H = Magnetic field strength (in A/m)
• l = Length of magnetic path (in meters)

But wait—how do we find H?

🔍 Finding Magnetic Field Strength (H)

H=B/μ0μr

Where:

• B = Magnetic Flux Density (Tesla)
• µ₀ = Permeability of free space
• µᵣ = Relative permeability of the material

So, AT=B/μ0μr×l

This is the full ampere-turns formula used in most magnetic circuit calculations.

📘 Simple Explanation with Keywords

Let’s say you have a magnetic core of certain length and area, and you want to create a specific amount of magnetic flux in it. You’ll need to calculate how strong the magnetic field must be, and how many coil turns and current (ampere-turns) are needed to produce that field.

✅ Final Summary

• Ampere-turns = The effort needed to create magnetic flux
• Use AT = H × l to find it
• Use H = B / (µ₀ × µᵣ) to find field strength
• Magnetic flux, flux density, reluctance, and permeability are all key parts of the magnetic circuit
• This concept is used in designing transformers, inductors, and electromagnet
  

compare series and parallel magnetic circuit

​

Series Magnetic Circuit

Imagine a road where one car moves through different sections — some smooth, some rough, and even a small bridge in between. No matter how the road changes, the same car keeps moving forward.

Just like that, in a series magnetic circuit, the same magnetic flux (φ) flows through every part of the circuit — even if each part is made of different materials.

🚦 What Is a Series Magnetic Circuit?

A series magnetic circuit is a closed path made of different materials, like iron or steel, and sometimes includes an air gap. These materials can have different sizes and different magnetic properties (called magnetic permeability).

But even though the parts are different, the magnetic flux stays the same throughout the circuit — just like the same amount of water flowing through different pipes joined one after another.

🧲 Important Terms to Know

• Magnetic Flux (φ): This is like the flow of magnetism in the circuit.
• Magnetic Path: The route taken by the magnetic flux.
• Reluctance (R): This is how much a material resists the flow of magnetic flux — just like resistance in an electric circuit.
• Magnetomotive Force (MMF or AT): This is the force that pushes the magnetic flux around the circuit, like voltage in an electric circuit.
• Permeability (μr): It tells how easily a material can carry magnetic flux.
• Air Gap: A small space filled with air in the magnetic path, which offers more reluctance because air is not a good conductor of magnetic flux.

📚 Simple Formula to Remember

If you have a circuit with 3 different materials and an air gap, the total reluctance is:

Total Reluctance = R1 + R2 + R3 + Rgap

Where:

• Each R = l / (μ0 × μr × A)
• l = length of the material
• μ0 = permeability of air (a fixed number)
• μr = relative permeability of the material
• A = cross-sectional area

And the Total Magnetomotive Force (MMF) is:

MMF = φ × Total Reluctance

Or:

MMF = H1 × l1 + H2 × l2 + H3 × l3 + Hg × lg

Where H = B / (μ0 × μr) and B is the magnetic field.

🔍 How to Calculate Step by Step

1. Find H (Magnetic Field Strength) for each part.
   • For magnetic materials: H = B / (μ0 × μr)
   • For air: H = B / μ0
2. Find the length (l) of each section of the magnetic path.
3. Find AT (Ampere-Turns) using:
   AT = H × l for each part.
4. Add all ATs to get the total AT needed for the full circuit.

🎯 Key Points to Remember

• In a series magnetic circuit, the magnetic flux (φ) is the same everywhere.
• Different materials offer different levels of reluctance.
• The total reluctance is the sum of all individual reluctances.
• The air gap increases reluctance a lot because it has low permeability.
• The force needed (MMF) depends on the total reluctance and the flux you want.

Introduction – What is an Air Gap?

In a magnetic circuit, sometimes we purposely leave a small empty space. This empty space is called an air gap. It may sound strange, but this small gap plays a very important role, especially in machines like electric motors, generators, and transformers.

Think of a magnetic circuit like a road where magnetic flux flows, just like cars on a highway. The iron core in the magnetic circuit helps the magnetic flux move easily. But sometimes, we need to add a tiny break in this road – that break is the air gap.

🔹 Why is an Air Gap Needed?

An air gap is necessary in many devices that use both electricity and magnetism (called electromechanical devices). Let’s understand it with a simple example:

In a motor or generator, there is a stator (the part that stays still) and a rotor (the part that rotates). The rotor needs space to move. So, we leave a small gap between the stator and the rotor. This gap is not a mistake – it is done on purpose so that the machine can work properly.

Without the air gap, the rotor cannot spin. And if the rotor doesn’t spin, the motor or generator won’t work.

🔹 How Does the Air Gap Affect the Magnetic Circuit?

Here comes the interesting part.

In a magnetic circuit, magnetic flux flows through both the iron part and the air gap. But there’s a big difference:

• Iron is a very good path for magnetic flux.
• Air is a bad path for magnetic flux.

This means the reluctance (opposition to magnetic flux) of air is very high, and the reluctance of iron is very low.

Even if the iron part is long, and the air gap is short, most of the effort (ampere-turns) is needed just to push the flux through the small air gap. That’s why engineers pay special attention to the air gap while designing magnetic circuits.

🔹 Important Formula (Explained Simply)

Let’s break this down simply:

• Reluctance of air gap = lg / (μ₀ × a)
• Reluctance of iron = li / (μ₀ × μr × a)

Where:

• lg = length of air gap
• li = length of iron part
• a = area of the cross-section
• μ₀ = permeability of free space
• μr = relative permeability of iron (very high)

Since μr for iron is more than 6000, its reluctance is very small compared to air.

👉 That’s why we often ignore the reluctance of iron and only focus on the air gap in calculations.

🔹 Key Points to Remember

• The air gap is a small but very important part of magnetic circuits.
• It is always required in motors and generators for mechanical movement.
• The magnetic reluctance of air is much higher than that of iron.
• Most of the ampere-turns (AT) in a magnetic circuit are used to push the magnetic flux through the air gap.
• Engineers often neglect the reluctance of iron in comparison to the air gap for easier and accurate calculations.

Parallel Magnetic Circuits

A parallel magnetic circuit is a magnetic path where the magnetic flux has more than one route to flow — just like in an electric circuit where current can go through more than one wire.

Think of it like this:
Imagine water flowing through a pipe. If you split that pipe into two smaller pipes, the water will divide and flow through both. In the same way, magnetic flux divides and flows through different magnetic paths.

This kind of setup is called a parallel magnetic circuit.

How It Works – Step by Step

Suppose we have a magnetic core shaped like a rectangle, and we wind a coil around one part of it. The coil has N turns of wire, and a current I flows through it. This setup creates a magnetic field and produces a flux φ₁.

Now here’s what happens:

• The flux φ₁ flows up to a point and then splits into two paths:
  • One part of the flux (φ₂) goes through path BE.
  • The other part (φ₃) takes a longer path BCDE.

So now, the total flux φ₁ = φ₂ + φ₃
These two paths BE and BCDE are in parallel, which is why we call it a parallel magnetic circuit.

What Is Needed to Drive the Flux?

To push magnetic flux through any material, we need something called magnetomotive force (MMF). It works just like voltage in an electrical circuit. It is calculated as:

MMF = N × I

Here,

• N = number of turns in the coil
• I = current flowing through the coil

But the magnetic material resists the flow of flux, and this resistance is called reluctance (like resistance in electric circuits).

Let’s say:

• S₁ is the reluctance of the first part of the core (before the split),
• S₂ is the reluctance of path BE, and
• S₃ is the reluctance of path BCDE.

Then the total MMF (magnetomotive force) required is:

NI = φ₁ × S₁ + φ₂ × S₂
Or
NI = φ₁ × S₁ + φ₃ × S₃

This means we need to calculate the flux in each part and multiply it by the reluctance of that part.

How Do We Calculate Reluctance?

Reluctance of any part is given by this formula:

Reluctance (S) = l / (a × μ₀ × μᵣ)

Where:

• l = length of the magnetic path
• a = cross-sectional area
• μ₀ = permeability of free space (a constant)
• μᵣ = relative permeability of the material

So each section of the magnetic circuit has its own reluctance depending on its size and material.

Why Are Parallel Magnetic Circuits Important?

Parallel magnetic circuits are used in many electrical machines and devices. Here’s why they matter:

• They distribute flux more efficiently.
• They allow for flexible magnetic circuit design.
• They help in reducing core losses in transformers and motors.
  

Magnetic Leakage and Fringing

In electrical machines like transformers and motors, magnetism plays a big role. But sometimes, not all of the magnetic force goes where we want it to go. Let’s understand this in a very easy way.

🔄 What is Magnetic Leakage?

Imagine a road made for cars. Now, some cars take a shortcut through the side streets instead of following the main road. The same thing happens in a magnetic circuit.

When we create magnetic flux (invisible lines of magnetic force), it should pass through a proper path, usually made of iron. But some of this flux “leaks” away into the air or other unwanted paths. This is called magnetic leakage.

👉 Useful Words to Remember:

• Total Flux (φᵢ) – The complete magnetic force produced
• Useful Flux (φ𝗀) – The part of magnetic force that goes through the right path (like the air gap in a machine)
• Leakage Flux (φₗₑₐₖ) – The part that escapes into the air or other unwanted space

So,
Leakage Flux = Total Flux – Useful Flux
That means,
φₗₑₐₖ = φᵢ – φ𝗀

📏 Leakage Coefficient:

To measure how much flux is leaking, we use this formula:
Leakage Coefficient = Total Flux / Useful Flux

Usually, this number is between 1.15 to 1.25 for most electrical machines.

🚫 Why is Magnetic Leakage Bad?

• It wastes energy
• It increases the size and weight of the machine
• It increases the cost
• It reduces efficiency

✅ How to Reduce Magnetic Leakage?

We can reduce magnetic leakage by keeping the magnetic coil (MMF source) very close to the air gap, so more flux goes through the correct path.

🌈 What is Fringing?

Now, imagine water flowing through a narrow pipe. At the open end, the water spreads out. Something similar happens with magnetic lines.

When magnetic lines pass through an air gap, they do not go straight. They bulge out at the edges. This is called fringing.

📌 Important Points About Fringing:

• Fringing increases the effective area of the air gap.
• As the area increases, the flux density (concentration of magnetic lines) decreases.
• Fringing is more if the air gap is long.
• Fringing is less if the air gap is short and wide.

👉 That’s why in real designs, we often add 10% extra to the air gap’s cross-sectional area to account for fringing.

🧲 Real-Life Use of This Knowledge

In devices like:

• Transformers
• Electric motors
• Inductors
• Relays

Understanding magnetic leakage and fringing helps engineers make these machines better, lighter, and more efficient.

🗝️ Easy Summary:

What is a Solenoid?

A solenoid is a long wire that is wound into a tight coil, one loop after another. Think of it like a spring made from wire. When electricity flows through this wire, something amazing happens—it creates a magnetic field just like a magnet!

The word solenoid comes from a Greek word that means “tube-like.” And that’s exactly what it looks like—a hollow tube made of coiled wire.

🔌 How Does a Solenoid Work?

When an electric current passes through the coil of the solenoid, it creates a magnetic field around it. This is a part of a bigger idea called electromagnetism—electricity creating magnetism!

Inside the solenoid, the magnetic field lines are straight and close together, which means the field is strong. Outside the solenoid, the field is much weaker and spread out.

We can understand the magnetic path in two parts:

1. Inside the solenoid – this part is long and straight.
2. Outside the solenoid – this part is small and weak.

Because the magnetic field inside the solenoid is much stronger, we usually only consider that part while doing calculations.

🧲 Magnetic Circuit of a Solenoid

The magnetic circuit is like the path that magnetic energy follows. In a solenoid, most of the magnetic energy stays inside the coil. That’s why we say the magnetic length is almost equal to the length of the coil itself.

Whether it’s an air-core solenoid or an iron-core solenoid, this idea stays the same.

👉 Using the Right-Hand Rule

To find the direction of the magnetic field in a solenoid, we use the right-hand rule:

• Wrap your right hand around the solenoid.
• Point your fingers in the direction of the current.
• Your thumb will point in the direction of the magnetic field inside the coil.

🧒 Real-Life Use of Solenoids (Easy Examples)

• Electric bells
• Car starters
• MRI machines
• Door locks
• Speakers

These are all powered by solenoids, making our everyday life easier!

✅ Final Words (Summary)

A solenoid is a simple but powerful tool. It shows us how electricity can create magnetism. It is used in many machines and devices we use every day. The coil of wire, the magnetic flux, and the current all work together to create a strong magnetic field.

It’s easy to understand and even easier to remember:
Electricity + Coil = Magnet

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