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Consider the mass spectrometer shown schematically

Math

Consider the mass spectrometer shown schematically. The electric field between the plates of the velocity selector is 950 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.930T.                Calculate the radius of the path in the system for a singly charged ion with mass m = 2.18x10-26 kg

a) The B-field in the velocity selector is out of the page (as indicated by dots). What is the direction of the electric field? Draw in a few field lines onto the diagram above.

b) Use your right-hand rule to determine the direction of the magnetic force acting on the moving charge assuming that it is positively charged? What is the direction of the electric force due to the electric field? To answer this question draw the free-body diagram for this positive charge while inside the velocity selector.  Label FB and FE onto the diagram.

c)In order for the charge to remain moving in a straight path in the velocity selector, what must be true?

d) What if it were a negatively charged ion.  Draw the free-body diagram below.  Will a negatively charged ion behave any differently?

e) Determine the velocity that the ion must have to emerge from the velocity selector un- deflected.  Show why a negatively charged ion will have the same speed based on the equation you used.  What if it were “doubly charged”?

f) Describe how the magnetic force is oriented relative to a positive ions speed, v once it enters the deflecting chamber.  A diagram would be sufficient.

g) Determine the equation of motion for the ion in the deflecting chamber and use it to solve for the radius of the path.

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