An ion source is producing 6Li ions, which have mass 9.99 ✕ 10−27 kg and charge...
An ion source is producing 6Li ions, which have mass 9.99 ✕ 10−27 kg and charge +e. The ions are accelerated by a potential difference of 15 kV and pass horizontally into a region in which there is a uniform vertical magnetic field of magnitude B = 2.4 T. Calculate the strength of the smallest electric field, to be set up over the same region, that will allow the 6Li ions to pass through undeflected.
Homework Answers
change in kinetic energy = change in electrical potential energy
= (potential difference)(charge)
(1/2)mv² = Vq
(1/2)(9.99e-27 kg)(v²) = (15000 V)(1.60e-19 C)
v = 6.931e5 m/s
net force = force on moving charges due to magnetic field
ma = qvB (v and B are perpendicular to each other)
m(v²/r) = qvB (centripetal acceleration)
r = mv/(qB)
r = (9.99e-27 kg)(6.931e5 m/s)/[(1.60e-19 C)(2.40 T)]
r =1.8e-2 m
d = 2r = 3.6e-2 m
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