Answer to Question #191601 in Field Theory for Kai

Question

A toroidal sample of magnetic material of susceptibility x = 2 × 10^-2 is wound with 100 turns of wire carrying a current of 2 A. The toroid is 0.10 m long.

(a) Find the solenoidal current density.(2)

(b) Determine the magnetic field intensity H produced by the current.(2)

(c) Calculate μ, the magnetic permeability of the material.(2)

(d) Calculate the induced magnetization M in the material.(2)

(e) Calculate the magnetic field B resulting from the current and the magnetization of the

material

Answer 1

Answer

A.

Current density

$j=\frac{I}{A}=\frac{2}{\pi (0.1) ^3}=63.69A/m^2$

B.

Magnetic field

$B=\frac{(1+x)NI}{2\pi R}$

$B=\frac{(1+0.2)(100)(2)}{2\pi (0.1)}=324.67T$

And

$H=\frac{B}{1+x}=\frac{324.67}{1+0.02}=318.3T$

C.

Magnetic permeability

$\mu=1+x=1+0.02=1.02$

D.

$M=Hx \\M=318.4\times0.02=6.5$

E.

Magnetic field we have calculated previously

$B=324.67T$