Question

A proton and an electron enter a uniform magnetic field. The velocity vector of each particle is perpendicular to the magnetic field. If their circular orbits have the same radii, what is the ratio of their speeds (Velectron/Vproton)? 5.5E-4 0.5 O 1.0 O 4.0 1800

Answer 1

particle is Q. Given that Proton (6) and electron (e) moves in same magnetic field. (which is perpendicular to motion of Both) When a charge charge particle (2) noving with speed (V) in the force on that charge magnetic field. The magnetic where e From = q VB sino angle between I and B U is perpendicular to B So o=go defects the path of particle into the circular both (say Radius R ). centripetal force QUB where h = mass of Particle OS For = 2VB The Fm The magnetic force on q on q mu R 2B = mu R R = my & 2BR 28 m for election Speed of electron -O Ve = he Bre me 2 for proton speed of Boton Up = & BRp me qe B Re the qe Re Up 2 B Rp ( qp Ro Both moves in path of same radius Ve me :) ( The me so Re = Rp FKMAH as

Ve 'Ze me me for Up ap electon and Boton, magnitude of charge is some 126 1=1211 -27 and -27 Ve Ve 1.67 X10 kg 22 (1.67 XIO = -31 lp Smp- i me = 9.1x10.9 kg 9.1X16-3 Ve Ve 0.18352 X 10 = 1835.2 1800 = 1800 Vp Up The ratio of their speed is 1800