# Motion of a charged particle in a magnetic field.

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 that the radius of curvature of the orbit of the alpha-particle is 10cm? Does the answer depend on the kind of medium it is emitted into?

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#### Solution Preview

Please see the attached file for a complete solution.

A radioactive source emits alpha-particles with kinetic energies of 4MeV. What must be the value of an applied magnetic field so that the radius of curvature of the orbit of the alpha-particle is 10cm? Does the answer depend on the kind of medium it is emitted into?

For a particle to move in a circular path with a constant speed a ...

#### Solution Summary

An alpha particle is moving in a magnetic field and the radius of curvature of the field is given. The strength of the magnetic field is calculated.

Motion of charged particle in uniform electric & magnetic fields

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 that is moving in a uniform electric field E = Ee_y and a perpendicular uniform magnetic field B = Be_z. Show that the equations of motion for the particle are:

(see the attached file for the equations)

(ii) If the particle is at rest at time t = 0, verify that the velocity components (see the attached file for the equations) satisfy the differential equations given in part (i) and the initial conditions.

(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 2). Photoelectrons are liberated from the plate at y=0 by ultraviolet radiation. 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 a negative y-direction. (Neither field is shown in Figure 2). The electric field is produced by a second infinite plate parallel to the first plate, maintained at a constant positive voltage V_0 with respect to the first plate. The separation of the plates is d.

Using the results of part (a), show that the electrons will fail to reach the second plate if (see the attached file for the equation) where -e and m are the charge and mass of an electron.

I am having difficulty with my maths and not arriving at all equations of motion/mass particularly mass in part a and I do not know what to chose at time t=0.

I am trying to use the Lorenz force.

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