Question 5.22: Referring to the electromagnet shown in Fig. 5.37, in which ......
Referring to the electromagnet shown in Fig. 5.37, in which the current I in the coil of N turns produces a uniform magnetic flux density B in the core, armature, and the gap with a cross section \mathcal{S}, express \pmb{F}_{m} on the armature in terms of B and \mathcal{S}.
Allowing a virtual displacement dℓ
of the armature in the upward direction, the magnetic energy in the gap is reduced by
dW_{m}= -2 \left[\frac{B^{2}}{2 \mu _{o}} \mathcal{S} dℓ\right] (5-143)
Inserting Eq. (5-143) into Eq. (5-140), and noting that d\pmb{l} = d ℓ\pmb{a}_{z} , where \pmb{a}_{z} is along the upward direction, we obtain
\pmb{F}_{m} \pmb{\cdot }d \pmb{l}= -d W_{m} (5-140)
\pmb{F}_{m}= \frac{B^{2}}{ \mu _{o}} \mathcal{S} \pmb{a}_{z} [N] (5-144)