- #1
cdummie
- 147
- 5
Homework Statement
If we have a system that is shown in the picture, the upper piece is magnet, and if we know the following data:
S = 1cm2 which is area of material, S0 = 1.2cm2 which is the area of fissure. To bring these tow pieces of this system magnetic induction in the fissure should be B0= 1.6 T. Dimensions of this magnetic circuit are: l1 = 15cm, l2 = 10cm, l0 = 1mm. Determine the force needed to bring together these two parts, and magnetic energy "wasted" to establish magnetic field right before bringing these two parts together.
Homework Equations
## w_m = \frac{1}{2}BH \\ F_m = - \frac{dW_m}{dx} ##
The Attempt at a Solution
density of magnetic energy is ##w_m = \frac{1}{2}BH## volume of both pieces of material together v=(l1+l2)S density of magnetic energy in fissures ##w_{m_0} = \frac{1}{2}B_0H_0## ,
volume of fissures ##v_0 = 2xS## (x instead of l0 because it changes when there two parts are getting closer, and force has only x component, which is the vertical one in this case). when the lower part in moving volume of fissure, magnetic energy of fissure and magnetic energy of part with material change, only the volume of part with material remains the same. But, if we say that flux is constant then, the only thing that affects the change of energy is the volume of the fissure.
## dW_m = B_0H_0Sdx \\ F_m = - \frac{dW_m}{dx} \\ F_m = 2SB_0H_0 ##
Since i have B0 i can easily determine H0 which would mean that i solved this without using the magnetization characteristics diagram. Am i doing something wrong?
Picture of magnet
Magnetic characteristics of material diagram.