CH-24 WEB - Chapter 24 Current and Resistance(Additional...

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Chapter 24 Current and Resistance (Additional Questions) 1) A steady beam of alpha particles ( 2 q e = + ) traveling with constant kinetic energy 20 MeV carries a current of 0.25 μ A. (a) If the beam is directed perpendicular to a plane surface, how many alpha particles strike the surface in 3.0 s? (b) At any instant, how many alpha particles are there in a given 20 cm length of the beam? (c) Through what potential difference is it necessary to accelerate each alpha particle from rest to bring it to an energy of 20 MeV? Solution: (a) The charge that strikes the surface in time t is given by q i t = ∆ , where i is the current. Since each particle carries charge 2 e , the number of particles that strike the surface is (b) Now let N be the number of particles in a length L of the beam. They will all pass through the beam cross section at one end in time t = L/v , where v is the particle speed. The current is the charge that moves through the cross section per unit time. That is, i = 2 eN/t = 2 eNv/L . Thus N = iL/ 2 ev . To find the particle speed, we note the kinetic energy of a particle is Since K = ½ mv 2 , then the speed is v = 2 / K m . The mass of an alpha particle is (very nearly)
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