Question

(1) Consider a proton with a kinetic energy of 1 GeV moving perpendicular to a magnetic field in the z-direction with Bo = 1000 nT. Find the proton speed, beta, gamma, total energy, the gyrofrequency, and the gyroradius. (2) Starting with problem 1, the field starts to increase with time (same direction though). B(t)=Bo(1+at), where a = 0.03)2.Bo. S20 is the gyrofrequency from problem 1 and is a constant. Find all the quantities asked for in problem 1, but now as functions of time. Also, what is the electric field?

Answer 1

According to the HomeworkLib policy I am advised to solve first question.thanks

Consider a proton with a kinetic energy aber nuova parpendicular to a mapmetic field w direction. Bo=1000nT. 19 (mv) qB Now The proton will satisfies. my quB nr 1x16x10 = 1.6 XI0 PE 16xjóla Paq Br. P = /2 x 16x109 x 1.67X10 27 Gyroradius = 8= 2.311721023 = 2.3117415 23 kg. m/s. 16X10 9 x 1000 x09 = 144.5 m. The speed of proton = q BY = 1.6*10 9 x 1000 x109 x 144.5 1.67X10 27 . =1.384610 mis E = '0000 4614 na Indi Total energy = E √ p2c2-morca = V 4,8x1029+ 3.35171020 = 1.580010 Jule. Time period ZITY 20x144-5 - 2 = .06556 See. V 1.3848104 Gan bonisy T 2011 2012144-5 Gero fregnly da + = 15.25 Ha. C 15.25 HZ.