New solution

naz edited
revision #18860 newer →
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+### Statement
+
+$10.1.25.$ [Insert the problem statement]
+
+### Solution
+
+To begin with, we will show the invariance of the sum in this case as well. The force acting on the electron inside the transition zone :
+
+$$F = -B_r e \upsilon_z$$
+
+Where $B_r$ is the radial component of induction, $\upsilon_z$ is the component of velocity along the axis of symmetry.
+
+$$\frac{dM}{dt} = -B_r e r \upsilon_z $$
+
+$$dM = - B_r e r dz$$
+
+Now let's consider the flow change through the cross section of a ring of arbitrary radius R:
+
+$$d\Phi = 2 \pi R B_r dz$$
+
+ From here:
+
+$$dM = -\frac{1}{2\pi}ed\Phi$$
+
+$$M+\frac{1}{2\pi} e \Phi = const$$
+
+Well, now, it's very easy to find the desired moment, at first the moment of momentum is zero, because the electron does not rotate:
+
+$$\frac{1}{2}eB_1 R^2 = M + \frac{1}{2}eB_2 R^2$$
+
+$$M = \frac{(B_2 - B_1)R^2e}{2}$$
+
+#### Answer
+
+[Insert a concise answer or boxed result]