2017 USA Physics Olympiad Exam Part B 9 Question B2 Beloit College has a "homemade"500 kV VanDeGraff proton accelerator,designed and constructed by the students and faculty. Accelerator dome (assume it is a sphere);accelerating column;bending electromagnet The accelerator dome,an aluminum sphere of radius a =0.50 meters,is charged by a rubber belt with width w 10 cm that moves with speed v=20 m/s.The accelerating column consists of 20 metal rings separated by glass rings;the rings are connected in series with 500 Mn resistors. The proton beam has a current of 25 uA and is accelerated through 500 kV and then passes through a tuning electromagnet.The electromagnet consists of wound copper pipe as a conductor.The electromagnet effectively creates a uniform field B inside a circular region of radius b=10 cm and zero outside that region. Metal rings of accelerating column Dome Glass separators Electromagnet Target wLLwLmLww白 Resistor Chain Only six of the 20 metals rings and resistors are shown in the figure.The fuzzy grey path is the path taken by the protons as they are accelerated from the dome,through the electromagnet,into the target. a.Assuming the dome is charged to 500 kV,determine the strength of the electric field at the surface of the dome. b.Assuming the proton beam is off,determine the time constant for the accelerating dome (the time it takes for the charge on the dome to decrease to 1/e1/3 of the initial value. c.Assuming the 25 uA proton beam is on,determine the surface charge density that must be sprayed onto the charging belt in order to maintain a steady charge of 500 kV on the dome. Copyright C2017 American Association of Physics Teachers2017 USA Physics Olympiad Exam Part B 9 Question B2 Beloit College has a “homemade” 500 kV VanDeGraff proton accelerator, designed and constructed by the students and faculty. Accelerator dome (assume it is a sphere); accelerating column; bending electromagnet The accelerator dome, an aluminum sphere of radius a = 0.50 meters, is charged by a rubber belt with width w = 10 cm that moves with speed vb = 20 m/s. The accelerating column consists of 20 metal rings separated by glass rings; the rings are connected in series with 500 MΩ resistors. The proton beam has a current of 25 µA and is accelerated through 500 kV and then passes through a tuning electromagnet. The electromagnet consists of wound copper pipe as a conductor. The electromagnet effectively creates a uniform field B inside a circular region of radius b = 10 cm and zero outside that region. Dome Metal rings of accelerating column Glass separators Electromagnet Target Resistor Chain Only six of the 20 metals rings and resistors are shown in the figure. The fuzzy grey path is the path taken by the protons as they are accelerated from the dome, through the electromagnet, into the target. a. Assuming the dome is charged to 500 kV, determine the strength of the electric field at the surface of the dome. b. Assuming the proton beam is off, determine the time constant for the accelerating dome (the time it takes for the charge on the dome to decrease to 1/e ≈ 1/3 of the initial value. c. Assuming the 25 µA proton beam is on, determine the surface charge density that must be sprayed onto the charging belt in order to maintain a steady charge of 500 kV on the dome. Copyright c 2017 American Association of Physics Teachers