# Magnetic Field around two magnetic boxes

#### DaniV

Problem Statement
Two magnets with magnetization Mz $\hat$ are placed on a surface parallel to
the xy plane, and are almost adjacent to each other, as illustrated. The
length and width of each magnet is w, the height is h, and the distance
between the magnets is d. w >> h >> d, and you can assume that w → ∞.
Find the magnetic field everywhere in space (above and below the magnets,
inside the magnets, and between them).
Relevant Equations
this question using fictive charge method:
the basic equation is $B=\mu_{0}(M\vec+H\vec)$
$\vec H =-\nabla\psi$
$\psi =\frac{1}{4\pi}\intagral \integral\integral\frac{\ro(x)_{fictive}}{|\vec x-\vec x`| }d^3x'$+\frac{1}{4\pi}\integral \frac{\sigma(x)_{fictive}}{|\vec x -vec x'|}dl'$I tried to look once at the zy axis and saw a two infinite capacitors with fictive charge density of M on the upper plane, and -M in the lower with a distance of h from each other, the two capacitors saparated with d in the y axis, but when I look in xy axis there was 2 another capcitors the first with the same fictive charge density M on the left and right plane with distance of d between them, the second one sapareted by h in the z axis show another capacitor with -M on the right and left planes how I preform such a superposition of fields because there are 4 planes and for which we can preform 2 different ways to look on the same problem (different capacitors) to find$\vec H\$?

#### Attachments

• 63.1 KB Views: 57
Related Advanced Physics Homework News on Phys.org

Homework Helper
Gold Member
2018 Award
This is kind of an odd problem. If $w >>h$ and $w>>d$, basically the magnetic field $\vec{B}$ will be zero everywhere. $\\$ The $H$ from the plus magnetic charges (fictitious) will (approximately) cancel the $H$ from the minus magnetic charges, except in the material where the $H=-M$, so that $B=\mu_o(H+M)=0$ also. I know I'm not supposed to furnish the answer, but that is the only way I can supply the necessary feedback here. $\\$ Note: on the faces parallel to the x-y plane, $\sigma_m=\vec{M} \cdot \hat{n}$, (comes from $-\nabla \cdot M=\rho_m$ and Gauss' law), and also $B=\mu_o(H+M )$ , with $\nabla \cdot H=- \nabla \cdot M$ gives with $H_{outside}=0$ that $H_{inside}=-M$, by Gauss' law. $\\$ Perhaps someone else may see a different solution, but this is what I get from working it.

### Want to reply to this thread?

"Magnetic Field around two magnetic boxes"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving