When a current flows in a wire, it creates a magnetic field around it. And, if the current-carrying wire is a coil, it creates a magnetic field that induces a voltage in it.
In other words, when the current-carrying conductor faces another magnetic field, it induces a force. And when a current-carrying conductor, moves in a magnetic field, it induces a voltage.
Magnetic field intensity around a closed path
Magnetic field intensity H is the ability of current to create a magnetic field in a circuit. To calculate the magnetic field intensity, caused by a current, we can use the below equation, Ampere’s law.
![](https://mechcollege.com/wp-content/uploads/2022/02/image-12.png)
If there is a ferromagnetic metal inside a coil, the magnetic field created by the coil is absorbed into the core.
![](https://mechcollege.com/wp-content/uploads/2022/02/image-13.png)
So, the Ampere’s law
![](https://mechcollege.com/wp-content/uploads/2022/02/image-14.png)
H is the magnitude of the magnetic field intensity vector,
![](https://mechcollege.com/wp-content/uploads/2022/02/image-15.png)
Magnetic field intensity and the core
If there is a ferromagnetic metal inside the coil, the magnetic field created by the coil is absorbed into the core. However, the strength of the magnetic field depends on the core.
![](https://mechcollege.com/wp-content/uploads/2022/02/image-16.png)
Total flux in a given area ϕ
![](https://mechcollege.com/wp-content/uploads/2022/02/image-18.png)
dA is the differential unit of area.
If the flux density is a constant and has a θ angle to a plane of area A, we can write the equation as,
ϕ =BA cos(θ)
If the flux density is perpendicular to the area and a constant, we can rewrite the above equation as,
ϕ = BA
So, to get to know the total magnetic flux generated by the current, we can substitute,
![](https://mechcollege.com/wp-content/uploads/2022/02/image-19.png)
Into the equation, therefore the magnetic flux density,
![](https://mechcollege.com/wp-content/uploads/2022/02/image-21.png)
Force that drives the current flow
In a normal electrical circuit, the voltage or the EMF (electromotive force) drives the current flow. So it can be described using Ohm’s law,
V=IR
But in magnetic circuits, the force that drives the current flow is MMF (magnetomotive force). And it’s represented by the script letter F and measured by Ampere turns. The equation for magnetomotive force is,
F=Ni
So, we can write the magnetic flux as,
![](https://mechcollege.com/wp-content/uploads/2022/02/image-22.png)
MMF, flux and reluctance
Magnetomotive force F (MMF) is the cause of the generation of magnetic flux ∅. Magnetic reluctance is a similar concept to electrical resistance. And the units of reluctance s ampere-turns per weber. Just like in Ohm’s law, we can build a relationship as follows,
![](https://mechcollege.com/wp-content/uploads/2022/02/image-24.png)
So, we can write the magnetic flux as,
![](https://mechcollege.com/wp-content/uploads/2022/02/image-25.png)
Reluctance in series
![](https://mechcollege.com/wp-content/uploads/2022/02/image-26.png)
Reluctance in parallel
![](https://mechcollege.com/wp-content/uploads/2022/02/image-27.png)
Permeance
As there is reluctance for the resistance, what is there for the conductance. There is permeance for the resistance.
![](https://mechcollege.com/wp-content/uploads/2022/02/image-28.png)