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One suggestion for an antimissile system has been to put an accelerator in space to make...

One suggestion for an antimissile system has been to put an accelerator in space to make a particle beam that could destroy missiles in flight. If the beam consisted of protons traveling at 31.6% of the speed of light, the protons would travel in a circular path of what radius (in km) in the earth's magnetic field? Take the magnetic field of the earth to be B = 50 μT. (For this reason, neutron beams would need to be used.)

Defined symbols:
   mp proton mass = 1.67 ×10–27 kg
   B the earth's magnetic field in μT
   s proton velocity in percent of the speed of light
   The answer is r, the radius of the proton's orbit


Hints:
    When you calculate the momentum, remember that relativistic mass increases my a factor of γ.
    Range of answers: 15 km to 40 km

r=?
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