How To Calculate a Magnetic Field

The law of gravitation tells us that there is a big Earth magnet that attracts us all to our planet. That is the reason why we don’t fall into outer space. But the discovery of that Earth magnet has not only explained why the apple falls. It also opened our understanding of the world of magnetic fields. In fact, our world almost revolves around different kinds of magnetic force. No wonder why there are now magnetic wires for radios, loop magnetic coils in electronics, and even magnet therapy in medicine. 

For the common people, only the applications of the magnetic field and the magnetic sensor matters. But for the sake of knowing, were you also intrigued as to how a magnetic field is calculated? Through a magnetic sensor, we can determine the presence and measure speed and strength of a magnetic field. We can always let the sensors do their work. But calculating the force in a magnetic field is possible with the devised formula.

Actually, different formulas for calculating a magnetic field are used in various conditions:

1.    A magnetic field is produced because of an infinite and straight current of filament.

B =  µo i/2π r

In this formula the B represents the magnetic field, r represents the radius in meters, i represents the current present in the wire, measured in amperes, and the µo is a constant permeability value that is equal to 1.26x10-6 H/m.

2.     Magnetic field is produced inside a straight line that is infinite and has an air core solenoid.

B = µo in

Still, B represents the magnetic field produced inside the solenoid. The µo is still the constant value 1.26x10-6 H/m, i is for the current present in the wire, measured in amperes, and n is how many turns the wire can do every unit length of solenoid. This is measured in 1/meters. 

In this special formula, the field’s direction should be parallel to the solenoid’s axis, and there should be no magnetic field present outside of the solenoid. 

3.     A magnetic field produced inside an air core, composed of a toroid coil.

B =  µo iN/2π r

The B still represents the magnetic field while the r represents the radius measured in meters. The mentioned constant value is still what the µo is representing. The current present in the wires, measured in amperes, is the i and the N is the number of turns that the toroid wire can make. 

4.     Magnetic field force created using the current from one circular loop.

B = ½  µo ib2(b2 + z2)-3 / 2

Similar symbols discussed above still work the same for this formula, only that the b is representing the radius of the circular loop while the z represents the distance from the loop’s plane to the loop point. 

If you’re not into mathematics, you will surely skip this page and won’t dare understand the meaning of these symbols. But whether you know these formulas or not, the calculations using them are still important to us as humans. 

You’re not required to memorize this—just leave the formula to the specialist. At least now, you have a slight understanding of how the force in a magnetic field is calculated through these formulas. And it just feels good to know something out of the ordinary. 


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