An electron of mass m and charge -e is moving through a uniform magnetic field \(\vec{B}=\left(B_{x}, 0,0\right)\) in vacuum. At the origin, it has velocity \(\vec{v}=\left(v_{x}, v_{y}, 0\right)\), where vx>0 and vy >0. A screen is mounted perpendicular to the x axis at a distance D from the origin.
The motion of the electron can be broken down into two parts:
1. constant motion in the x direction plus
2. a periodic part, the projection of which in the yz plane is circular. Find the angular velocity w of the electron associated with the circular component of its motion. Express the magnitude of the angular velocity in terms of Bx, the magnitude of the electric charge e, and other known quantities.
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...
A cat rides a merry-go-round turning with uniform circular motion. At time t1 = 2.00 s, the cat’s velocity is given by vx = 3.00 m/s and vy = 4.00 m/s. At t2 = 5.00 s, the cat’s velocity is given by vx= −3.00 m/s and vy = −4.00 m/s. Take the coordinate system of the merry-go-round to have its origin at the center. (a) What is the magnitude of the cat’s centripetal acceleration? (b) What is the magnitude of...
A cat rides a merry-go-round tuning with a uniform circular motion. At t1= 2.00 s, the cat's velocity is given by vx= 3.00 m/s and vy= 4.00 m/s. At t2= 5.00 s, the cat's velocity is given by vx= -3.00 m/s and vy= -4.00 m/s. Take the coordinate system of the merry-go-round to have its origin at the center. (a) What is the magnitude of the cat's centripetal acceleration? (b) What is the magnitude of the cat's average acceleration during...
Active Figure Motion of a Charged Particle in a Uniform Magnetic Field The animation below illustrates a charged particle moving in circular motion due to the magnetic force caused by a constant and uniform magnetic field oriented into the page. The blue crosses represent the tails of the magnetic field vectors nstructions: Use the blue sliders to adjust the mass, speed, particle charge and magnetic field magnitude. Change each parameter and observe the eftect on the particle's motion. If the...
(#966932-48) (Motion of Charge in Field) D2 (Motion Perpendicular to Field) A proton of mass mp-1.67 × 10-27 kg and a charge of gp-1.60 x 10-19 C is moving through vacuum at a constant velocity of 10, 000 m/s directly to the east when it enters a region of uniform electric field that points to the south with a magnitude of El =2.83e+3 N/C . The region of uniform electric field is 5 mm wide in the east-west direction. How...
Part A In a region of space, a magnetic field points in the +x-direction (toward the right). Its magnitude varies with position according to the formula B = Bo + bx, where Bo and b are positive constants, for 3 > 0. A flat coil of area A moves with uniform speed v from right to left with the plane of its area always perpendicular to this field. What is the emf induced in this coil while it is to...
A particle undergoes uniform circular motion. This means that it moves in a circle of radius R about the origin at a constant speed. The position vector of this motion can be written Here, analogous to the simple harmonic motion problem of HW 1, ω is the angular frequency and has units of rad/s 1/s and can also be written in terms of the period of the motion as 2π (a) Show that the particle resides a distance R away...
3. Circular Motion in a Magnetic Field See Figure 2. A particle of charge +e and mass m is accelerated from rest by a potential difference V. The particle then enters a region of uniform magnetic field B perpendicular to the velocity. The particle will undergo uniform circular motion. It instead, the charge is doubled and the mass is quadrupled, while keeping both the potential difference and strength of the magnetic field the same, i) how does the radius of...
Help me solve this question asap nfluenced by magnetic An electron moves following a circular path in vacuum i field. The radius of the electron's path is 2.0 x 102 m, magnetic field strength is 2.0x 10-2 T, and specific charge electron e/m is-I .76 x 1011 C kg" (b) i. Write an expression for angular velocity of electron. ii. Calculate its orbital period ii. What happen to the electron's path when its velocity decreases? [10 marks]