Mass Spectrometer: In the picture to the right, a charged ion (charge q) is acce

Question

Mass Spectrometer: In the picture to the right, a charged ion (charge q) is accelerated by an electric field and then enters a region where the magnetic field, B, is uniform and points out of the page as shown. The ion follows the circular arc shown and is detected a distance 2R from where it entered. Explain roughly why the ion curves to the left, why the a horizontal row of path is circular, and why its speed does not change. particle detectors An object, like this ion, moving at a constant speed v along an arc of constant radius R must have an acceleration vector of magnitude a = v^2/R and pointing toward the center of the circle. Use Newton's 2nd Law along with this formula for the acceleration and the formula for the magnetic force on a moving charge to find a relation between R,v,B, and m. If there is a whole row of detectors, and all ions enter with the same speed, which ones will find the particles with largest mass?

Explanation / Answer

a)

due to centripetal force , particle move in a circular path.

centripetal force is provided by the magnetic force =q(v x B)

due to magnetic force , speed of the particle remains unchange. because direction of force is perpendicular to velocity of the particle.

b)

because

centripetal force is provided by the magnetic force =q(v x B)

mv2/R =qvB

R =mv/qB

here mass is directly proportional to the mass.

so largest mass is depends on the radius of curvature of the particle (if speed and charge of the ions is same)

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