Question

Was just wondering if someone could help me with this please.

The Large Haron Collider (LHC) is the world's largest particle accelerator. It is circular in formation, with a radius of 4.2429 km. Protons can be made to travel around it in opposite direc tions, and then collide head on. Its operation depends on many individual electromagnets. To help understand the proton motion, you may wish to use this interactive simulation of a charged particle moving in a magnetic field: https://teaching.smp.uq.edu.au/fiveminutephysica/index.html course-phys1002Rlecture Moving Charges (a) Assume that protons that are injected into the LHC are travelling at 31.1% of the speed of light. They have achieved this speed via a linear accelerator.) What force and what magnetic field would be required to constrain the motion of the protons to a circular path that fits the dimensions of the LHC? Ensure that you specify both the magnitude and the direction of the magnetic field that a proton would need to experience. Use diagrams to show how magnetic field could be used to make a proton travel (i) clockwise and (ii) anticlockwise. (6) At peak operation, the protons circulate around the path 11,245 times per second. What is the required magnetic field strength then? (c) One type of electromagnet used in the LHC is a solenoid 15 m long, which creates a magnetic field of 6.0 T when a current of 8,500 A flows through its wiring. How many turns make up this solenoid? Part B (Advanced) In actuality, the LHC does not have a simple, single circular path. () Protons that are travelling in opposite directions usually move in concentric paths with rilii that differ by 0.30 m. Investigate the implications of this for the magnetic field that would be required to keep them moving in uniform circular motion. Also compare the instrument's magnetic fields (as discussed so far) to the Earth's magnetic field, and discuss implications for the design of the facility. (1) Devices are included to accelerate the protons while they are circulating around. As the proton speed is increased, what else must be controlled to ensure that a proton orbits at the desired raulius? Explain your answer. (c) How could you make the counterpropagating protons collide? - give a conceptual argument.

Answer 1

For the next option - in actual particle accelerators there are two seperate tubes for protons at travel in opposite directions and at the place of collosion they are at same place. So as there is less change in radius at opposite travel magnetic field magnitude change is less but direction would be opposite. From question we see required field is 23 milli Tesla while earth's magnetic field is .25 to .65 Gauss where at one Tesla equals to 10000 Gauss.

Solution for charged particle in magnetic field centepetal force is balanced by Lorentz force + mv que tenen x xadius of circulax bich. U velocity perpendicular to promote B magnetic field. q charge of particle Here velocity 31.4% 07 C, 94.800.000 m/s. r = 4.2429 km = 4242.9m. . 9 = 1.6x10 - 19 c m = 1.67x10-27 kg (proton? B= mu = 1.67X10 27 x 94200000 = 2.31x10 " T Er 1.6810 19 X 4242.9 Now viang sighit hand sule, on clockwise motion, magnetic field downward penito page and on counterclock wise magnetic field coming above of plane of page Now 11945 turns in a second vclocity = 11245x 2XT1 X 4242.9 = 299627637.94mis This is relativstic case, using mass formula. for u= 0.99c. m= smo = 1 mo with mo= 1.67X10 27 kg. = 1 1.67810-27 = 1.183 x 10 20 kg. JI-109912 = r = 1.183410 x 299627657.94 1.6810 19 X 42 42.9 = 5.22X103T B= Mon I, on = X total tutns - B = HONI = BL = 6x15 = 8425 turns 47810 7x8500 using formula Ho

In actual there are lots of things in particle accelerator, magnetic field is only for directing the beam of particles while electric field is used for accelerating the particles. Many slits and filters are also used.

For colliding counterprotons again magntic field is used to take them at the place of collision.