Charged Particle in Constant Electromagnetic Field, Lorentz

The motion of a charged particle in an electromagnetic field can be obtained by the Lorentz Equation for the force on a particle in such a field. If the electric field vector is E and the magnetic field vector is B, the force on a particle of mass m that carries a charge q and has a velocity v is given by:

a.) If there is no electric field and the particle enters the magnetic field in a direction perpendicular to the lines of flux show that the trajectory is a circle with radius:

r = (mv)/(qB)

b.) Choose thr z axis to lie in the direction of B and let the plane containing E and B be the xy plane.

Then: B = Bk, E= Ey j + Ez k

Show that z(t) = zo = zo't + (qEz)/(2m) t2

Where z(0) = zo and z'(0) = zo'

c.) Continue the calculation and find x'(t) and y'(t); show that the time averages of these velocities are:
(x') = Ey/B, (y') = 0

d.) Integrate the velocitiy equations above (c) with the initial conditions:

The motion of a chargedparticle in an electromagnetic field can be obtained from the Lorentz equation for the force on a particle in such a field.
If the electric field vector is E and the magnetic 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.

Please see the attached file. Please solve with explanations included.
Two chargedparticles are traveling in circular orbits with the same speed in a region of uniform magnetic field that is directed into the page, as shown. The magnitude of the charge on each particle is identical, but the signs of the charges are unequal.

See attached file for diagram.
Please solve and explain.
Three chargedparticles are injected into a uniform magnetic field -- all of the particles have the same speed, but their masses and charges are different. Which of the following statements are true?
1. (T/F) Particle #2 is negatively charged
2. (T/F) If they

Which of the following statements are true about magnetic forces acting on charged or unchargedparticles? Choose True or false for the following statements.
True False the magnetic force always acts parallel to the direction of motion of the moving chargedparticle.
True False the maximum magnetic force that a charged

I need a perfect step by step solution of the following problem:
A particle of charge q is started at the origin with an initial velocity (vector)v_0 = v_0 x(^), in a region where a uniform electric field exists (vector)E = E_0 z(^), and a magnetic field intensity is given by (vector)B = B_0 x(^) + B_0 y(^). HINT: ROTATE TH

The average intensity of sunlight reaching the earth is 1390 W/m^2. A charge of 2.6 x 10^-8 C is placed in the path of this electromagnetic wave. (a) What is the magnitude of the maximum electric force that the charge experiences? (b) If the charge is moving at a speed of 3.7 x 10^4 m/s, what is the magnitude of the maximum m

Full question is attached.
1) In this question we will consider the motion of a chargedparticle in uniform electric and magnetic fields that are perpendicular. You may ignore the effects of gravity throughout this question.
a)
i) Consider a chargedparticle of mass m and charge q which is moving in a uniform electric field

1. In an experiment with cosmic rays, a vertical beam of particle that have charge of magnitude 3e and mass 12 times the proton mass enters a uniform horizontal magnetic field at 0.250 T and is bent in a semicircle of diameter 95.0 cm
a) Find the speed of the particles and the sign of their charge.
b) Is it reasonable to ignor

I cannot figure out what equations to use or how to set up the following problem. It just seems like there is some data missing that i need. Any insight as to where to start would really help!
A radioactive source emits alpha-particles with kinetic energies of 4MeV. What must be the value of an applied magnetic field so th