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Calculating the strength of the magnets in the LHC watch

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    The LHC is currently being built at CERN in Geneca to collide two beams of protons head-on. Each beam will have protons of energy 7TeV. The particle accelerator is approximately circular witha radius of about 1.4km. Assuming the whole circular path of the protons takes place in a uniform magnetic field, calculate the strength of the magnets needed to maintain the protons inside the beam-pipe.

    Ok, so i tried equating the centripetal force and the lorentz force

    mv^2/r=qvB
    mv/r=qB and got v from kinetic energy formula,
    0.5mv^2

    but this gave me 683*10^6 T. From a little browsing i found the right answer should be about 8.36T
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    (Original post by EmmaK90)
    The LHC is currently being built at CERN in Geneca to collide two beams of protons head-on. Each beam will have protons of energy 7TeV. The particle accelerator is approximately circular witha radius of about 1.4km. Assuming the whole circular path of the protons takes place in a uniform magnetic field, calculate the strength of the magnets needed to maintain the protons inside the beam-pipe.

    Ok, so i tried equating the centripetal force and the lorentz force

    mv^2/r=qvB
    mv/r=qB and got v from kinetic energy formula,
    0.5mv^2

    but this gave me 683*10^6 T. From a little browsing i found the right answer should be about 8.36T
    what did you get v ?
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    (Original post by EmmaK90)
    ...
    I think you need to use the fact that at 7TeV, the protons are basically relativistic. The kinetic energy is defined to be the difference between the total relativistic energy and the rest mass, but in this case the Kinetic energy >> rest mass and so you can approximate that E=pc.
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    r = mv/bq-----> b = mv/rq----> v = (2E/m)^1/2 convert eV to Joules. Convert Radius to meters...... that should give you the answer.
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    I got v as 2.688*10^6. that was with the radius in meters, and the energy converted to joules. this gave 2.75*10^-5T. i forgot to change the energy to joules. but this is still wrong, so i guess i have to do it relativisticly. E=pc => p=E/c=3.792*10^-23... where do i go form here?
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    (Original post by EmmaK90)
    The LHC is currently being built at CERN in Geneca to collide two beams of protons head-on. Each beam will have protons of energy 7TeV. The particle accelerator is approximately circular witha radius of about 1.4km. Assuming the whole circular path of the protons takes place in a uniform magnetic field, calculate the strength of the magnets needed to maintain the protons inside the beam-pipe.

    Ok, so i tried equating the centripetal force and the lorentz force

    mv^2/r=qvB
    mv/r=qB and got v from kinetic energy formula,
    0.5mv^2

    but this gave me 683*10^6 T. From a little browsing i found the right answer should be about 8.36T
    I can't help with the calculation, unfortunately, but were the figures you're working on given to you? The radius of the LHC is about 4.3km (it's about 27km in circumference).
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    (Original post by boromir9111)
    r = mv/bq-----> b = mv/rq----> v = (2E/m)^1/2 convert eV to Joules. Convert Radius to meters...... that should give you the answer.
    At 7TeV its relativistic so you can't use that energy formula.
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    (Original post by EmmaK90)
    I got v as 2.688*10^6. that was with the radius in meters, and the energy converted to joules. this gave 2.75*10^-5T. i forgot to change the energy to joules. but this is still wrong, so i guess i have to do it relativisticly. E=pc => p=E/c=3.792*10^-23... where do i go form here?
    Well you know p/r =qB

    Edit: You need to be careful with the units here again
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    Oh, if you can't use that then i got no idea!!!!!.... maybe "suneilr" can just enlighten us and give the formula needed!!!!
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    (Original post by suneilr)
    Well you know p/r =qB

    Edit: You need to be careful with the units here again
    hmmm.. this gave 1.69*10^-7T. probably gone wrong with units somewhere
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    The way you think about centripetal forces also changes at relativistic speeds (the apperance of mass in the centripetal force formula suggests this, I guess), so this question is quite a pain in the ass.
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    (Original post by EmmaK90)
    hmmm.. this gave 1.69*10^-7T. probably gone wrong with units somewhere
    p=7*10^{12} eV/c = \frac{7*10^{12}*1.6*10^{-19}}{3*10^8} J/(ms^{-1})

     B=\frac{p}{qr} = \frac{7*10^{12}*2\pi}{27*10^3*3*  10^8} = 5.43T
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    oh god, i forgot about that bit this problem sheet is just stupidly hard.
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    (Original post by suneilr)
    p=7*10^{12} eV/c = \frac{7*10^{12}*1.6*10^{-19}}{3*10^8} J/(ms^{-1})

     B=\frac{p}{qr} = \frac{7*10^{12}*2\pi}{27*10^3*3*  10^8} = 5.43T
    thank you!
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    (Original post by EmmaK90)
    thank you!
    No problem. You're not at Imperial by any chance? I swear I had a question exactly like this a while back....
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    nah, i'm at warwick
 
 
 
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