Question

2. Total Current Density The magnetic field , B, in a ferromagnetic material is a known function of spatial coordinates. (a) Prove that the total (conduction plus magnetization) volume current density in linear material, total = + m, can be expressed in terms of B as follows: total = x B/MO. (b) Specifically, compute total for B(x,y,z) = (2x +z)/y28+ (2/y)ý + (x + 2y)2 T. (c) In a uniform Ē field, assume there exists a volume current density T (not necessarily constant). Determine the magnetization current density in terms of B and ). (d) Use Matlab and B as in 2b to symbolically determine the total current density and thus verifying your answer to part 26 (Hint, you may wish to take advantage of MATAB's pretty function. (feel free to attempt this problem in Python, however, it is not easy to obtain symbolic results with Python).

Answer 1

following sdution as Accoding to the above given Question by the sol al thui unum of the material al Col The follows: Gursent density write the formula for conduction volume Current density. JE TXH +(0) Here magnetic magner field in density vector is H write the formula for meg ne ti za tion volume Current density ze Im = xm →@ Here, Mais the magnetization vector The relation between magneti jahon vector and magnetic field M = (M1-12 4 intensity vectol, Here, Mr is the relative permeability The relation between magnetic field inensity vector and the magnetic Hux density, Veitoy. Scanned with CamScanner

Here M * the permeability the formula for relative par mability. Here, Mo + the Ab Solute pomitivity The formula for total volume Current density. Frot = 5+ Ims] Sub the Corre sponding values from quatton (and (al The = (х н+ аху) 5 784 + ex (Hr-13 14 = p X( 4 +(-1) ] soxu (1+Hr+1] = tx Bforl WMO Irod - DX BLI is thus, the 40 401 volume Current density vector is fpx Blue) Scanned with CamScanner THO

(6) Determine the total volume Current density of the material fd a material for agiven inlue or regnetle flux denſity vected as followe: The formula fel total volume Current density, J = 7 X BI Here magnetic flux Density vector is B Sub the corresponding values. pr@y) Â T: Ox You Cavett) +€9+la ay}] * * {0-09 - 4, 438-| Yo te oy videos 1 - 445 44 +3 = %[af - 4) ona pot :: The total volume Current densing vecot is a The totame Scanned with CamScanner