The figure shows a mass spectrograph that is operated with deuterons, which have

Question

The figure shows a mass spectrograph that is operated with deuterons, which have a charge of +e and a mass of 3.34 times 10^-27 kg. The deuterons emerge with negligible velocity from the source, which is grounded. The speed of the deuterons as they pass through the accelerator grid is 8.0 times 10^5 m/s. A uniform magnetic field of magnitude B = 0.20 T, directed out of the plane, is present to the right of the grid and is perpendicular to the velocity of the deuterons. The deuterons make a circular orbit in the magnetic field. What is the radius of this orbit, and what is the initial direction of their deflection just as they enter the magnetic field? (e = 1.60 times 10^-19 C)

Explanation / Answer

apply centripetal force = magnetic force

i.e mv^2/r = qvB,

so speed v = sqrt(2eV/m)

where m = mass o the charged particle

v = velocity, r = radius ,

q = charge = 1.6*10^-19 C

B = magnetic field

so now , so as r = mv/qB

r = (3.,34e -27 * 8 e 5)/(1.6 e -19 * 0.2)

r = 8.35 cm

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