Question

Doctor Crusher arrives at the new Enterprise Sick Bay and sees a brand new mass spectrometer has been installed. Captain Picard says the technicians did not get time to calibrate it, so Doctor Crusher will have to calibrate it herself. Commander LaForge provides Doctor Crusher with some antiprotons to test the mass spectrometer. Antiprotons have the same mass as a proton, but are negatively charged. Doctor Crusher sets the electric and magnetic fields such that the antiprotons leave the velocity selector at a speed of 3.0 x 106 m/s. The magnetic field, as viewed from overhead of the mass spectrometer is 0.40 Tesla pointing toward you, and the antiprotons are initially moving to the right within the velocity selector. If the magnetic field continues at the same magnitude and direction within the detection area, how long will it take to hit the sensor (it needs to make a semi-circle)? (10 points) As viewed from above, which direction will the antiproton initially deflect? (5 points) What is the voltage required in the velocity selector to select for the velocity stated? (5 extra credit points)

2.2 Doctor Crusher arrives at the new Enterprise Sick Bay and sees a brand new mass spectrometer has been installed. Captain Picard says the technicians did not get time to calibrate it, so Doctor Crusher will have to calibrate it herself. Commander LaForge provides Doctor Crusher with some antiprotons to test the mass spectrometer. Antiprotons have the same mass as a proton, but are negatively charged. Doctor Crusher sets the electric and magnetic fields such that the antiprotons leave the velocity selector at a speed of 3.0 x 106m/s. The magnetic field, as viewed from overhead of the mass spectrometer is 0.40 Tesla pointing toward you, and the antiprotons are initially moving to the right within the velocity selector. If the magnetic field continues at the same magnitude and direction within the detection area, how long will it take to hit the sensor (it needs to make a semi-circle)? (10 points) As viewed from above, which direction will the antiproton initially deflect? (5 points) What is the voltage required in the velocity selector to select for the velocity stated? (5 extra credit points)

Answer 1

question BK B=BO = BR que x BK towards rie Velocity selecta magnetic field Bk - 0.40 Terla ( in î direction sime po antiprotan is morning towards right side, son The magnetie field afflict force on postiche a globo qobl-f). To Balance, this force electric field mist act in ty direction, so that pestice keeps moving Without right any deflection Equilibsium cardation q, v B = ge (gE is the force due to electric field and qobi is due to Magneticofield V=BE. 3X 106 m/s and B=0,40 T. E = v 3x106 7.5X106 Volt/m B 10.4 This gives

that lo, electric field of magnitude 7.5x 10 Vattulm is required ty direction so particle leaves velocity News, at it leancy welocity selectos, oly magnetic field is present perpendicular to the helocity is. and B = Bk. This will lead the particle to move in circle so, ( for circular motion) mua qub Ir=mo 9B After covering semicirall, antiproton will hit the wall so, T= Distance speed T- Ar XX mv qB X V TTE AM 9B T = (3.14) X (1,6 7X1022) 6 [1:6 X 10-19) X0.40. I = 8,193 X 10-8 seu

do after 8.19X10-8 sec, antipeston will hit the wall. When antiproton is placed, magnetic field will not apply 8o initially the force gE will only act and as for antiprotan, charge negative. antibsoten will more ofposite to electric field, ie in Ih direction. So, we neill see from above stat initially, pasticle mill deflect to apdeds direction. But, as it gains relocity magnetic force acts and equilibelum 80, - he g Voltage required in velocity selector Voltage - £.£X distance. Electric field is calculated in ④ and distance is Cheldth) of relocity selector is not given in question