If Instead of extruded ring with constant magnetization, then there is an object with a magnetic pole density is given as -
m = - . = 0
And a surface density of magnetic pole strength is given as -
m = .
To calculate the magnetic scalar potential (*) and () from given equations as :
* = (1 / 4) m dA' / | - ' |
= - 0*
By symmetry, on axis must be given as -
= Bz (z)
= - 0 (d* / dz) { eq.1 }
Using cylindrical coordinates (, , z), then we have
* (z, =0) = *1 + *2
* (z, =0) = (1 / 4) (M ' d' d') / [,2 + (z - l/2)2]1/2 + (1 / 4) -(M ' d' d') / [,2 + (z + l/2)2]1/2
* (z, =0) = (M/2) ' d' / [,2 + (z - l/2)2]1/2 - (M/2) ' d' / [,2 + (z + l/2)2]1/2
* (z, =0) = (M/2) {[(D/2)2 + (z - l/2)2]1/2 - [(d/2)2 + (z - l/2)2]1/2 - [(D/2)2 + (z + l/2)2]1/2 - [(d/2)2 + (z + l/2)2]1/2}
Now, using eq.1 & we get
= - 0 (d* / dt) |z=0
= - (0 M / 2) { (-l/2) / [(D/2)2 + (l/2)2]1/2 + (l/2) / [(d/2)2 + (l/2)2]1/2 - (l/2) / [(D/2)2 + (l/2)2]1/2 + (l/2) / [(d/2)2 + (l/2)2]1/2}
= 0 M { l / [(D2 + l2)]1/2 - l / [(d2 + l2)]1/2 }
A uniformly magnetized (M -M) extruded ring, as shown, has inner diameter d and outer diameter...
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