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

Question

You have landed a great summer job in the medical school assisting a research group investigating short-lived radioactive isotopes, which might be useful in fighting cancer. Your group is working to transport 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 expected to decay quickly, it is important to know precisely how much time it will take to transport the alpha particles. Your job is to design 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 degrees using a magnetic field. The beam will be traveling horizontally in an evacuated tube. Where the tube is to make a 90 degree 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 degree turn.

Explanation / Answer

Related Equations: cyclotron formula q/m = v/BR (1) constant speed d/t = v (2) Remember: A charged particle's motion in a magnetic field is constant speed motion. That is, no change in speed but definitely there is a change in direction. We wish to find time. so from (2) t = v/d Note, we wish to find the time spent by the particle turning 90degrees. What is the distance of that path? A full 360deg is the circumference of the circle, 2PiR, so a 90degree turn is a quarter of that. that is d = Pi*R/2 (i hope you understand why) Now, let's just plug this to equation (2) t = 2v/Pi*R We dont know R and v yet, and we have only one equation left, equation (1). Luckily, equation 1 expresses this two as a quotient, from eq 1 q/m = v/BR -------------> v/R = qB/m plugging to eq 2 t = 2qB/Pi*m That's it, just plug the values. If you can't use equation 1, I think the derivation of that will be easy and presented in most books. Starting from Lorentz force law: F = qE + qv x B

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