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Prove that a charged particle entering a strong uniform magnetic field experiences specular reflection, if its speed is below some limiting value (the "magnetic mirror" principle, Fig. 28.20). Find the kinetic energy of the electrons which experience specular reflection, if the electron beam is perpendicular to the magnetic mirror" magnetic field with an induction B= 0.1 T is established in a large region, the thickness of the magnetic mirror" is d= 10 cm.

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Solution :A charged particle entering a magnetic field perpendicularly to the lines ur induction will move ALONG tho are of a circle of radius `R =p//eB,` where `mu` is the momentum of the particle, Mirror rellectiontakes PLACE if the entire PATH of the particle happens to lie inside the field.
Since, according to the conditions of the problem, the electrons move perpendicularly to the "magnetic mirror" they will be reflected backwards, provided that the radius of the semicircle is less than the thickness of the "mirror" Hence `p/(e B) lt d`.
The total energy of the electron is `epsi=sqrt(epsi_(Psi)^2+l^(2) c^2) lt sqrt(e_(v)^2)+e^2B^2a^2c^2)`the kinetic energy is K `=epsi-epsi_(0)`. Finally, we get `K lt epsi_(0) (sqrt(1+(eBd//m_(e)c)^2)-1)`


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