Question #171005

Consider a particle of charge Q, moving perpendicular to a magnetic field of flux density B with a velocity v. 


A) Electrons are accelerated through a potential difference of 2000 V. Calculate their kinetic energy in J.

B) Calculate their speed.


C)If they enter a magnetic field of flux density 1.5 mT, what will be the radius of the circle that they will move in


1
Expert's answer
2021-03-16T08:41:10-0400

(A)

KE=qΔV=1.61019 C2000 V=3.21016 J.KE=q\Delta V=1.6\cdot10^{-19}\ C\cdot2000\ V=3.2\cdot10^{-16}\ J.

(B)

KE=12mev2,KE=\dfrac{1}{2}m_ev^2,v=2KEme=23.21016 J9.11031 kg=2.65107 ms.v=\sqrt{\dfrac{2KE}{m_e}}=\sqrt{\dfrac{2\cdot3.2\cdot10^{-16}\ J}{9.1\cdot10^{-31}\ kg}}=2.65\cdot10^7\ \dfrac{m}{s}.

(C) Applying the Newton's Second Law of Motion, we get:


qvB=mev2r,qvB=\dfrac{m_ev^2}{r},r=mevqB,r=\dfrac{m_ev}{qB},r=9.11031 kg2.65107 ms1.61019 C1.5103=0.1 m.r=\dfrac{9.1\cdot10^{-31}\ kg\cdot2.65\cdot10^7\ \dfrac{m}{s}}{1.6\cdot10^{-19}\ C\cdot1.5\cdot10^{-3}}=0.1\ m.

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