the motion of a particle in uniform electric and magnetic fi

Full question is attached.
1) In this question we will consider the motion of a charged particle in uniform electric and magnetic fields that are perpendicular. You may ignore the effects of gravity throughout this question.

a)
i) Consider a charged particle of mass m and charge q which is moving in a uniform electric field E = Eey and a perpendicular uniform magnetic field B = Bez. Show that the equations of motion for the particle are,

ii) If the particle is at rest at time t = 0, verify that

iii) Hence determine the position of the particle at time t, assuming that it was located at the origin at t = 0

b) An infinite metal plate occupies the xz-plane (y=0). The plate is kept at zero potential, V = 0. (see figure 1 below) Photoelectrons are liberated from the plate at y = 0 by ultravioletradiation. The initial velocity of the photoelectrons is negligible. A uniform magnetic field B is maintained parallel to the plate in the positive z-direction and a uniform electric field E is maintained perpendicular to the plate in the negative y-direction. The electric field is produced by a second infinite plate parallel to the first plate, maintained at a constant positive voltage V0 with respect to the first plate. The separation of the plated is d.

Themotion of a charged particle in an electromagnetic field can be obtained from the Lorentz equation for the force on a particle in such a field.
If theelectric field vector is E andthemagnetic field vector is B the force on a particle of mass m that carries charge q and has velocity v is given by:
F = qE +qv X B
1.

A particle undergoes uniform circular motion of radius 26.1 μm in a uniformmagnetic field. Themagnetic force on theparticle has a magnitude of 1.60 x 10-17 N. What is the kinetic energy of theparticle?

An electron moves in a force field due to a uniformelectric field E and a uniformmagnetic field B that is at right angles to E. Let E = jE and B = kB. Take the initial position of the electron at the origin with initial velocity vo = ivo in the x direction. Find the resulting motion of theparticle. Show that the path of motio

A positively charged particle of mass 7.28E-8 kg is traveling due east with a speed of 85.7 m/s and enters a 0.290 T uniformmagnetic field. Theparticle moves through one-quarter of a circle in a time of 2.08E-3 s, at which time it leaves the field heading due south. All during themotiontheparticle moves perpendicular to the

An electron that has velocity v = (2.0 x 106 m/s)i + (3.0 x 106 m/s) j moves through theuniformmagnetic field B = (0.030 T)i - (0.15 T)j.
a) Find the force on the electron.
b) Repeat your calculation for a proton having the same velocity.

A charged particle moves through a velocity selector at a constant speed in a straight line. Theelectric field of the velocity selector is 3.25 103 N/C, while themagnetic field is 0.360 T. When theelectric field is turned off, the charged particle travels on a circular path whose radius is 4.20 cm. Find the charge-to-mass rat

In this question we will consider themotion of a charged particle in uniformelectricandmagnetic fields that are perpendicular. You may ignore the effects of gravity throughout this question.
(a)(i) Consider a charged particle of mass m and charge q that is moving in a uniformelectric field E = Ee_y and a perpendicular u

Question 1: An infinitesimal current element Idl is located at the point x = 0.05m, y =0, z = 0 in a cartesian coordinate system. The current element points in the direction of the positive z-axis and has magnitude 2x10^-6 A m. Calculate the magnitude and direction of themagnetic field due to this current element at the point

A charged particle travel ling to the right (assume in the plane of the paper) is injected into an area in which themagnetic field is directed out toward you. What will be the resulting motion of theparticle? How much work will themagnetic field do on the charged particle as a result? Explain.
Does themotion move in a cir