9.3.12 | правка #18470 | Решения Савченко

Statement

9.3.12. Thin square plates with dimensions $$a \times a \times h$$ $$(h ≪ a)$$ are magnetized to saturation in the direction
perpendicular to their plane. In the center of each plate is the magnetic field induction $$B_0$$ . What will
be the field induction inside a long rectangular column of section $$a \times a$$ assembled from these plates?

Solution

From the solution to problem 9.2.19, we know that the magnetic moment of such a thin plate is $M=\frac{B_0\pi a}{2\sqrt{2}\mu_0 h}$
We also know that $$i=M$$ , and the induction inside the infinite rod is $B=\mu_0 i$ (see previous problems).
Hence:
$B=\frac{B_0\pi a}{2\sqrt{2}h}$

Answer

$B=\frac{B_0\pi a}{2\sqrt{2}h}$