Magnetic Flux Vs. Magnetic Flux Linkage: Comparative Analysis And Facts

In this article, we will be comparing magnetic flux vs. magnetic flux linkage to understand the difference between them.  

Magnetic flux and flux linkage have quite different meanings, magnetic flux vs magnetic flux linkage. When we talk about magnetic flux, we are referring to the total number of field lines passing through a surface, and in the case of flux linkage, it is associated with the total number of turns. 

Suppose we have a conducting wire with the area A and the magnetic field strength is B. Again, the magnetic lines are falling at a theta. Therefore the magnetic flux becomes:

Φ= B.A

Φ= B A cos θ

Now what we do is turn this conducting wire into coils with 5 turns. In this case, flux linkage becomes: 

λ= N Φ

λ= 5Φ

So this example makes it clear to us about the magnetic flux vs. magnetic flux linkage. Further, on the one hand, we have magnetic flux as scalar and flux linkage as vector. The unit of magnetic flux is weber, and that of flux linkage is weber-turns. 

Magnetic flux vs magnetic flux linkage
Image Credit: Wikipedia

What is magnetic flux linkage surface?

The flux linkage is often confused with magnetic flux. Many consider it to be equal to magnetic flux, but in actuality, it is the extension of the magnetic flux. The loop of the coil is the surface of magnetic flux linkage through which flux is passed. 

For the surface with area A, the magnet flux linkage becomes:

λ= N Φ

λ= N B A

What is the magnetic flux through a closed surface?

As per the Gauss Law of magnetism, we get the magnetic flux through a closed surface. It states that the flux through a closed surface is always equal to zero. 

This is because, through a closed surface, the number of magnetic field lines going in will be equal to the total magnetic lines going out. That is why the total magnetic flux becomes zero through a closed surface. 

What is magnetic flux linkage equation?

According to Faraday’s Law, the change in magnetic flux linkage induces the emf, i.e., electromotive force. This law provides us with the equation of magnetic flux linkage. Therefore the equation becomes:

ɛ  = -d/dt

Here we can see the equation difference of magnetic flux vs magnetic flux linkage. By substituting the value of λ we get:

ɛ = – dNΦ/dt

ɛ = -N dΦ/dt

Magnetic flux linkage formula with angle

The flux linkage formula, as we have seen, is NΦ. Now, if we substitute the formula of magnetic flux in the flux linkage formula, we will get magnetic flux linkage with angle. 

The formula of magnetic flux is given by Φ = B A cos Φ. Substituting this formula in the above formula of flux linkage, we get: 

λ = N B A cos θ


N is the number of turns

B is the magnetic field

A is the area 

θ is the angle the magnetic field makes with the plane. 

So, using the above formula, we find magnetic flux with an angle. It was all about magnetic flux vs magnetic flux linkage.

Frequently Asked Questions (FAQs)

What is magnetic flux?

The flux provides us with the number of anything passing through anything. 

Magnetic flux gives us the number of the magnetic field that passes through a given surface. It has only magnitude and thus a scalar. Phi is used to represent the magnetic flux. Thus its formula is

Φ= B. A and unit is weber. 

What is magnetic flux density?

As the name suggests, the magnetic flux density provides the density. 

The total perpendicular magnetic flux per unit area gives us the magnetic flux density. The magnetic flux density is usually represented by B. The unit magnetic flux density is weber m2 or Tesla. 

What is flux linkage?

The flux linkages link the magnetic flux with the turns of the conductor. 

When you transform the conductor into turns, then we get flux linkage λ as NΦ. Here Φ is the magnetic flux. It is the change in flux linkage that induces a current in the magnet.

Explain magnetic flux vs magnetic flux linkage. 

The magnetic flux and flux linkage are usually confused, but they differ. Let us understand magnetic flux vs magnetic flux linkage.

The magnetic flux provides us with the information of the total magnetic field coming in or out of the surface. On the other hand, the magnetic flux linkages link this magnetic flux with the turns of a conducting coil.

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