The motion 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 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.

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

r = mv/qB = v/w

where w=gB/m is the cyclotron frequency

2.
Choose the z-axis to lie in direction of B and let the plane containing E and B be the yz-plane.
Thus:
B = Bk E = E_y j + E_z k

Show that the z-component of the motion is given by:

z(t) = z(0) + (z_dot(0))*t+(qE_z / 2m) * t^2

3.
Continue the calculation and obtain expressions for dx/dt and dy/dt Show that the time average of these velocity components are:

<dx/dt> = E_y/B <dy/dt> = 0

4.
Integrate the velocity equation from (3) and show (with appropriate initial conditions - see attached file) that:

A particle of charge 6e enters a region containing a magneticfield with a velocity of 7.5 X 105 m/s that is perpendicular to the field. There is a force on the particle of 6.84 X 10-13 N. Find the magneticfield T.

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 uniform magneticfield. The particle 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 the motion the particle moves perpendicular to the

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

Full question is attached.
1) In this question we will consider the motion of a charged particle in uniform electric and magneticfields 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

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Please explain and solve problem.

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

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Does the motion move in a cir

Please see the attached file. Please solve with explanations included.
Two charged particles are traveling in circular orbits with the same speed in a region of uniform magneticfield 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.

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 magneticfield so th