Mathematical and Physical Journal
for High Schools
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# Problem P. 4480. (November 2012)

P. 4480. In a long straight coaxial cable the centre conductor has a radius of r1, and the outer metallic shield has an inner radius of r2, and an outer radius of r3. (Between the two conductors there is a dielectric insulator.) In the two conductors the current of I flows in the opposite direction. Determine the magnetic induction vector B around the cable as a function of the distance r measured from the symmetry axis of the cable.

(4 pont)

Deadline expired on December 10, 2012.

Sorry, the solution is available only in Hungarian. Google translation

Megoldásvázlat. A mágneses indukció (a végtelen hosszú, egyenes vezető teréhez hasonlóan) ,,érintőleges", nagysága

$\displaystyle B(r)=\frac{\mu_0 I}{2\pi}\cdot \frac{r}{r_1^2},\qquad \text{ha}\qquad 0\le r\le r_1,$

$\displaystyle B(r)=\frac{\mu_0 I}{2\pi}\cdot \frac{1}{r},\qquad \text{ha}\qquad r_1\le r\le r_2,$

$\displaystyle B(r)=\frac{\mu_0 I}{2\pi}\cdot \frac{r_3^2-r^2}{(r_3^2-r_2^2)r},\qquad \text{ha}\qquad r_2\le r\le r_3,$

$\displaystyle B(r)\equiv 0,\qquad \text{ha}\qquad r_3\le r.$

### Statistics:

 23 students sent a solution. 4 points: Barta Szilveszter Marcell, Bingler Arnold, Büki Máté, Jenei Márk, Juhász Péter, Kollarics Sándor, Medek Ákos, Pristyák Levente, Sisák Mária Anna, Szilágyi 585 Dezső, Sztilkovics Milán, Ürge László, Vajda Balázs, Varju Ákos. 3 points: Antalicz Balázs, Czipó Bence, Sárvári Péter. 1 point: 6 students.

Problems in Physics of KöMaL, November 2012