Question

A coil of wire 0.12 m long and having 340 turns carries a current of 13 A. (a) What is the magnitude of the magnetic field strength H (in A/m)? (b) Calculate the flux density B (in tesla) if the coil is in a vacuum. (c) Calculate the flux density (in tesla) inside a bar of metal positioned within the coil that has a magnetic susceptibility of 1.90 x 10-4. (d) Calculate the magnitude of the magnetization M (in A/m).

Answer 1

To solve this problem it is necessary to apply the concepts related to the magnetic field

the flux density and the magnitude of the magnetization.

Each of these will be tackled as the exercise is carried out, for example for the first part we have to:

Part A) Magnitude of the magnetic field

$H = \frac{NI}{L}$

Where,

N = Number of loops

I = Current

L = Length

If we replace the given values the value of the magnitude of the magnetic field would be:

$H= \frac{340*13}{0.12}$

$H = 36833 A\cdot turns/m$

For the second and third part we will apply the concepts of density both in vacuum and positioned at a point, like this:

PARTE B) Flux density in a vacuum

$B = \mu_0 H$

Where,

$\mu_0 =$ Permeability constant

$B = (4\pi*10^{-7})(36833)$

$B = 0.04628T$

PART C) To find the Flux density inside a bar of metal but the magnetic susceptibility is given

$X_m = 1.9*10^{-4}$

$\mu_R = 1+X_m$

$\mu_R = 1.00019$

Then the flux density would be

$B = \mu_0 \mu_R H$

$B = (4\pi*10^{-7})(1.00019)(36833)$

$B = 0.04629T$

PART D) Finally, the magnetization describes the amount of current per meter, and is given by the magnetic susceptibility, that is:

$M = X_m H$

$M = 1.9*10^{-4}*36833$

$M = 6.996A/m$