Правка разделов «Statement», «Answer»
en/9.3.14.md
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| @@ -1,7 +1,10 @@ | |||
| ### Statement | |||
| − | $9.3.14.$ | ||
| + | $9.3.14.$ A disk of radius $R$ and height $h ≪ R$, made of a material with magnetic permeability $µ = 1 + κ$, $κ ≪ 1$, | ||
| + | was placed across a uniform magnetic field of induction $B_0$. How much will the induction in the center | ||
| + | of the disk differ from $B_0$? | ||
| + | |||
| ### Solution | |||
| Under the influence of an external field, a magnetic moment of magnitude is induced in a paramagnet $M=\chi H$,where $H$ - | |||
| magnetic intensity associated with $B$ | |||
| by ratio $B = \mu \mu_0 H$, | |||
| due to small size of $\chi$, $$M\approx \frac{B_0\chi}{\mu_0}$$ | |||
| As we know, the disk field at its center can be replaced by the ring current field $I = Mh$, | |||
| which is equal to $$B=\frac{\mu_0 I}{2R}$$, this is the desired change in the field, we substitute:$$\Delta B=\frac{B_0\chi h}{2R}$$ | |||
| @@ -15,4 +18,4 @@Solution | |||
| #### Answer | |||
| − | [Insert a concise answer or boxed result] | ||
| + | $$\Delta B=\frac{B_0\chi h}{2R}$$ | ||
| @@ -1,7 +1,10 @@ | |||
| ### Statement | ### Statement | ||
| $9.3.14.$ |
$9.3.14.$ A disk of radius $R$ and height $h ≪ R$, made of a material with magnetic permeability $µ = 1 + κ$, $κ ≪ 1$, | ||
| was placed across a uniform magnetic field of induction $B_0$. How much will the induction in the center | |||
| of the disk differ from $B_0$? | |||
| ### Solution | ### Solution | ||
| Under the influence of an external field, a magnetic moment of magnitude is induced in a paramagnet $M=\chi H$,where $H$ - | Under the influence of an external field, a magnetic moment of magnitude is induced in a paramagnet $M=\chi H$,where $H$ - | ||
| magnetic intensity associated with $B$ | magnetic intensity associated with $B$ | ||
| by ratio $B = \mu \mu_0 H$, | by ratio $B = \mu \mu_0 H$, | ||
| due to small size of $\chi$, $$M\approx \frac{B_0\chi}{\mu_0}$$ | due to small size of $\chi$, $$M\approx \frac{B_0\chi}{\mu_0}$$ | ||
| As we know, the disk field at its center can be replaced by the ring current field $I = Mh$, | As we know, the disk field at its center can be replaced by the ring current field $I = Mh$, | ||
| which is equal to $$B=\frac{\mu_0 I}{2R}$$, this is the desired change in the field, we substitute:$$\Delta B=\frac{B_0\chi h}{2R}$$ | which is equal to $$B=\frac{\mu_0 I}{2R}$$, this is the desired change in the field, we substitute:$$\Delta B=\frac{B_0\chi h}{2R}$$ | ||
| @@ -15,4 +18,4 @@Solution | |||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | $$\Delta B=\frac{B_0\chi h}{2R}$$ | ||