P29_021

# P29_021 - 21. So that the magnetic ﬁeld has an eﬀect on...

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Unformatted text preview: 21. So that the magnetic ﬁeld has an eﬀect on the moving electrons, we need a non-negligible component of B to be perpendicular to v (the electron velocity). It is most eﬃcient, therefore, to orient the magnetic ﬁeld so it is perpendicular to the plane of the page. The magnetic force on an electron has magnitude FB = evB , and the acceleration of the electron has magnitude a = v 2 /r. Newton’s second law yields evB = me v 2 /r, so the radius of the circle is given by r = me v/eB in agreement with Eq. 29-16. The kinetic energy of the electron is K = 1 me v 2 , so v = 2K/me . Thus, 2 r= me eB 2K = me 2m e K . e2 B 2 This must be less than d, so 2m e K ≤d e2 B 2 or 2m e K . e2 d2 If the electrons are to travel as shown in Fig. 29-33, the magnetic ﬁeld must be out of the page. Then the magnetic force is toward the center of the circular path, as it must be (in order to make the circular motion possible). B≥ ...
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## This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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