In a mass spectrometer it is important to control the properties of the charged

Question

In a mass spectrometer it is important to control the properties of the charged particles in order to obtain the most accurate results. Inside a spectrometer there is a region (inside the box) into which charged particles travel with a variety of speeds, v, as shown. Assume that you have the appropriate controls and can create constant magnetic and electric field in this region in whichever direction and with any strength you choose (Neither of the fields are zero.) The incoming particles have mass m, charge q, and a range of speeds v. You want to choose appropriate electric and magnetic fields (strengths and directions) to select only charged particles with the particular speed v_0 such that the particle will travel "straight through" and not be deflected. What are the direction(s) of your selected electric and magnetic fields? What is the ratio of the electric and magnetic field strengths that you chose? Express your answer in terms of particle properties. What happens to particles that are moving with a speed greater than v_0? What happens to particles that are moving with a speed less than v_0?

Explanation / Answer

part a:

assumption: charge is positive. (for negative charge, both electric and magnetic force will alter direction and hence there wont be any net effect)

electric force is along electric field and magnetic force is along cross product of velocity and magnetic field

if electric field is in +ve y direction (perpendicular to the direction of motion)

then in order to make magnetic force along -ve y direction, magnetic field has to be in +ve z direction ,(out of the page of the paper)

if electric field is in -ve y direction, magnetic field has to be into the page of the paper.

part b:

electric force=q*E

magnetic force=q*v0*B

then q*E=q*v0*B

==>E/B=v0

part c:

if a particle is moving with speed greater than v0, magnetic force will be higher

and it will get deflected in the opposite direction of the electric field

part d:

if speed is lesser than v0, electric force will be higher and it will get deflected along the direction of electric field

in both part c and part d, the particle will collide with the appartus and wont pass "striaght through

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