calculator:force_between_magnetic_cup_and_plate
Calculator of force between a magnetic cup holder and a steel plate
 | Stan Zurek, Calculator of force between a magnetic cup holder and a steel plate, Encyclopedia Magnetica, http://e-magnetica.pl/doku.php/calculator/force_between_magnetic_cup_and_plate, {accessed: 2025-03-13} |
This calculator provides force between flat magnetic holder constructed from a coin-like permanent magnet placed in a ferromagnetic steel cup. The calculations are based on deriving the reluctance of the magnetic circuit due to non-magnetic gaps between the magnet and the edge of the cap, to the steel plate.
| Magnetic force F acting on the thick steel plate due to magnet in a steel cup holder | ||
|---|---|---|
| Source: These equations were derived (not published elsewhere) by Stan Zurek from the assumption of constant magnetic flux through all parts of the magnetic circuit. | ||
| $$ F = \frac{ {B_m}^2 · A_m + {B_c}^2 · A_c }{ 2 ⋅ µ_0 } $$ | (N) | |
| where: | ||
| Bm in the gap under magnet | Bc in the gap under the edge of the cup | |
| $$ B_m = \frac{ B_r · L_m }{ Lm + g_m + g_c · \frac{A_m}{A_c} } $$ | $$ B_c = \frac{ B_r · L_m }{ ( L_m + g_m ) · \frac{A_c}{A_m} + g_c } $$ | (T) |
| and: | ||
| Am area of the pole of the magnet | Ac area of the edge of the cup | |
| $$ A_m = \frac{ π }{4} · {D_m}^2 $$ | $$ A_c = \frac{π}{4} · (OD^2 - ID^2) $$ | (m2) |
| and: $B_r$ - remanence (T) of the magnet, $D_m$ - diameter (m) of the magnet, $L_m$ - length (m) of the magnet, $g_m$ - non-magnetic gap (m) between the magnet and the steel plate, $OD$ - outer diameter (m) of the steel cup, $ID$ - inner diameter (m) of the steel cup, $g_c$ - non-magnetic gap (m) between the edge of the cup and the steel plate | ||
Interactive calculator
S. Zurek, E-Magnetica.pl, CC-BY-4.0
Notes: This calculator gives only an approximation of an order of magnitude of expected force, and it is applicable only for thin layers positioned close to the cup holder surface. The calculation is suitable only for flat magnets (Dm > Lm) and for small gaps (g ≪ Dm). It is also assumed that the cup is not saturated magnetically.
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calculator/force_between_magnetic_cup_and_plate.txt · Last modified: 2025/01/24 10:45 by stan_zurek