Yet another magnetic calc

🇷🇺 🇬🇧

To make good magnetic knife holders (when the magnet is hidden inside the wood), it is necessary to choose the magnet itself and the depth at which it is hidden (i.e., the distance from the magnet to the front surface of the knife holder). Changing the depth even by a small distance can affect how strongly the knife is attracted. It is rather painful to determine the depth and dimensions of magnets by trial and error, that's why this calculator was created.

Calculations are given for the most common neodymium magnets in the shape of a disk. It is suggested to set the diameter D, disk thickness H, and depth L (distance from the front surface of the holder to the recessed magnet).

Magnet grade Residual magnetic induction Magnet diameter in mm (D) Magnet thickness in mm (H) Distance to magnet in mm (L) Knife weight in grams

Calculations

On a magnetic holder, the knife is subjected to: the force of attraction F_g, the magnetic attraction force F_m, and the friction force between the blade and the wood. In this case, the friction force can be neglected. The gravitational force acting on the knife can be calculated as follows:

F_{g} = m \cdot g = 0.250 kg \cdot 9.8 {m/s}^{2} = 2.45 newtons

Thus, for the knife to be held securely, it is necessary for F_m to be significantly greater than F_g. To calculate the force of magnetic attraction, you can use the following formula:

F_{m} = \frac{B^{2} \cdot S}{2 \cdot μ_{0}}

B: magnetic flux density
S: area of the round face of a magnet in meters $PI \cdot R^{2} = 0.00017671458676442585$
μ₀: Relative magnetic permeability for vacuum $4 \cdot Pi \cdot 10^{-7} = 0.0000012566370614359173$

The magnetic flux density must first be calculated using the formula:

B = \frac{B_{r}}{2} \cdot (\frac{H + L}{\sqrt{R^{2} + (H + L)^{2}}} - \frac{L}{\sqrt{R^{2} + L^{2}}})

B_r: remanent magnetic induction
H: magnet thickness
L: distance
R: magnet radius

Let's plug in the numbers and get

B = \frac{1.3050000000000002}{2} \cdot (\frac{8 + 3}{\sqrt{{7.5}^{2} + (3 + 8)^{2}}} - \frac{3}{\sqrt{{7.5}^{2} + 3^{2}}}) = 0.29678092486087215 tesla

Then you can substitute the numbers and calculate F_m:

F_{m} = \frac{{0.29678092486087215}^{2} \cdot 0.00017671458676442585}{2 \cdot 0.0000012566370614359173} = 6.193048876964624

Got F_m = 6.193

Conclusion

It has been empirically deduced that in order to confidently hold the knife on the magnetic holder, it is necessary that F_m is about 3 times greater than F_g. Thus, the following conclusion can be drawn from the calculated figures: : The magnet is strong enough for this knife

Calculations

Conclusion

References