A 10.0-cm length of wire has mass 5.0 g and is connected to a source of emf by l

Question

A 10.0-cm length of wire has mass 5.0 g and is connected to a source of emf by light, flexible leads. A magnetic field B 0.5 T is horizontal and perpendicular to the wire. Find the current necessary to float the wire, that is, the current for which the magnetic force balances the weight of the wire. Particles of charge q and mass m are accelerated through a potential difference Delta V and enter a region of uniform magnetic field B perpendicular to their velocity. If r is the radius of their circular orbit, show that q/m = 2 Delta V/r2B2. A mass spectrograph uses a velocity selector consisting of parallel plates separated by 2.00 mm and having a potential difference of 160 V. The magnetic field between the plates is 0.42 T. The magnetic field in the mass spectrograph is 1.2 T. Find (fl) the speed of the ions entering the mass spectrograph and (b) the separation distance of the peaks on the photographic film for 238U+ (mass 3.95 times 10"35 kg)and 235U+ (mass 3.90 times 10 -25 kg). A certain cyclotron has a magnetic field of 2.0 T and is

Explanation / Answer

d = 2.00 mm, V = 160 V, B = 0.42 T
B' = 1.2 T, m1 = 3.95*10-25 kg, m2 = 3.90*10-25 kg, q = 1.6*10-19 C

a) E = V/d = 8.00*104 V/m

speed v = E/B = 1.90*105 m/s

b) qvB' = mv2/r, so r = mv/qB'

separation = 2(r1 - r2) = 2(m1 - m2)v/qB' = 0.20 m

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