Anti-Matter Cosmic Ray Detector An international consortium is presently buildin

Question

Anti-Matter Cosmic Ray Detector

An international consortium is presently building a device to look for anti-matter nuclei in cosmic rays to help us decide if there are galaxies made of anti-matter. Anti=matter is just like ordinary matter except the basic particles (anti-protons and anti-electrons) have opposite charge from ordinary matter counterparts. (anti-protons are negative, and anti-electrons are positive).

A schematic of the device is shown below. A cosmic ray -- say a carbon nucleus or an anti-carbon nucleus -- enters the device at the left where its position and velocity are measured. It then passes through a (reasonably uniform) magnetic field. Its path is bent in one direction if the charge is positive, the opposite direction if the charge is negative. Its deflection is measured as it goes out of the device.

a. On the figure shown, what is the direction of the magnetic field? How do you know?

b. What is the path (i.e. the mathematical shape) followed by each particle in the device? Why?

c. If you were given the magnetic field, B, the size of the device, D, the amount of charge on the incoming particle, q, and the mass of the incoming particle, M, would this be enough to calculate the displacement of the charge, d? If so, describe briefly how you would do it (but don't do it). If not, explain what additional information you would need (but don't estimate it).

device shown at the right. and velocity are m at the left where its position directio uniform) magnetic field. Its path is bent in one ion if its charge is negative. Its deflection is measured as path of anti-matter particle (anti- carbon nucleus) path of matter position and particle (carbon nucleus) position velocity detection plate detection plates own, what is the direction of the magnetic field? Ho

Explanation / Answer

Part a

As force on a charged particle in magnetic field, f = q(v cross B).

Clearly from here we can say that if B is pointing outward from the plane of paper then using the right hand curl rule the direction of force on the positive particle will be towards the direction which is shown in the figure. Hence the direction of magnetic field is outward from the plane of paper.

Part b

As the f is constant hence acceleration will also be constant along the direction of deflection while it is 0 for perpendicular direction. So this motion is just similar to the motion of a projectile on earth and hence trajectory will be like that of a projectile which basically is parabolic.

Part c

No, we can’t do that.

As here force, f = qvB.

Mass = m.

So acceleration along deflection, a = f/m = qvB/m

Using kinematics relations, vf2 - vi2 = 2ad or d = vit + at2/2, we can see that first we need to know velocity v and then either we need final velocity or some means to calculate time. Only then we can calculate d.

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