Question

2. Consider a charged particle in a magnetic field. Let -e = -1.60 x 10-191C) be an electron, under B=0.1T) of a uniform magnetic field directed out of the page direction (o-direction). At t = 0[sec] the particle is at the origin, and the initial velocity is toward positive y direction. (a) Sketch the initial configuration of this electron (-e at the origin) into (x,y)-plane. Applying the right hand rule, indicate the magnetic force on this moving electron. Note that an electron carries negative charge. (b) Combine Newton's second law with the radical acceleration a = [m/sec), write the equation of motion, where r is (undetermined) radius of the or- bit, v is undetermined) velocity of an electron, and m is the mass of an electron. The absolute value of magnetic force on a charge -e is given by evB. (Note; write a symbolic expression for equation of motion.) (c) Determine the radius of this motion, if the initial velocity is lu = 1 x 10" [m/sec), that is, solve the equation of motion for r and substitute Jul = 1 x 10 m/sec), m= 9.11 x 10 kg) and other given numbers. (d) Determine the absolute value of the velocity, if the radius of this motion is r = 0.1m (e) Suppose the radius of this motion is r = 0.1 m). Determine the period of this circular motion. Note that the period T[sec satisfies v x T = 2nr. Next, consider a microwave oven which has f = 2450[MH2) = 2.45 x 10°/1/s] frequency. (f) Determine the angular velocity w = 27. (g) What magnitude-field strength B is required for -e to move in circular orbit with this frequency. (Hint; w = v/r, and B does not depend on r.) (h) If the microwave oven emits f = 2500 MHz), what magnetic field strength B is needed for a circular orbit?

Answer 1

-Y According to right hand reele direction of magnetic force on electron is towards - Veux-axis 16 force on electron due to magnetic field B. - f = e.V.B - 0 . But f=ma. =) Famxol lei le Compaccing equin n and equin® - eJB = moet The = me © but v = 1227 = 1x107m8, m=9.11810-3119 B= 0.1 I e = 1.6x1019.c in equm ® I we will get-

de = 9.11X1031x 18107 __1.681019x0o_ = L = 5.69x104m | fut le = o.lm, M=9.11X16311g, e-lbriotyc B20.) I in equn ☺ Oil = 9.11X103y ze (1:6x1079)x011 = 24 = 0:1X16X169 xo) 9.11 x 1031 = 72 =.1.756 x 109 mis (According to theory of relativety this velocity is not possible because it is greater than Velocity of light (3x10&m[)) @ V XT = 2tile T= 2TH = 2x3.14 XO:) 1 v . 1.7568109 T= 3.576x1010