You have landed a great summer job in the medical school assisting in a research

Question

You have landed a great summer job in the medical school assisting in a research group investigating short lived radioactive isotopes which might be useful in fighting cancer. Your group is working on a way of transporting alpha particles (Helium nuclei) from where they are made to another room where they will collide with other material to form the isotopes. Since the radioactive isotopes are not expected to live very long, it is important to know precisely how much time it will take to transport the alpha particles. Your job is to design that part of the transport system which will deflect the beam of alpha particles (m = 6.64 x 10-27 kg, q = 3.2 x 10-19 C) through an angle of 90 by using a magnetic field. The beam will be traveling horizontally in an evacuated tube. At the place the tube is to make a 90 turn you decide to put a dipole magnet which provides a uniform vertical magnetic field of 0.030 T. Your design has a tube of the appropriate shape between the poles of the magnet. Before you submit your design for consideration, you must determine how long the alpha particles will spend in the uniform magnetic field in order to make the 90-turn.

Explanation / Answer

Bsically u need the alpha partical make angle a 90degree turn given the above condition

this is 1/4 of a full revolution negleting gravitational force is only the magnetic force

on the partical Fb =qvB and the partical centriptal acceleration a = v^2/r where r is the

radius of circulr trajectory

= qvB = mv62/R R = mv/qB for the partical to move one full revolution the time is

T = 2ar/v = 2a/v * mv/qB = 2am/qB

so for 1/4T which is a 90degree turn

the time is 1/4(2am/qB)

= 1/2* a(6.64*10^-27kg)/(3.2*10^-19c)*(0.030T)

= 1.09*10^-6s = 1.09micr s

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