The equations of motion for a particle of mass m and electrical charge q under the...
3. A particle of mass m, charge q, and inital velocity vo is injected into uniform electric field E, find the position trajectory for the motion of the particle. Only after arriving at the vector equations for the trajectory, find the position of the particle after 5s, when E - 2i - 3j +4k vo- (2i -3j + 4k)1000 1.0 × 10-3 6.02 x 1023 q-1.6 x 10-19 (mass of a single H+)
A charged particle with mass M and charge q moves in the x – y plane. There is a magnetic field of magnitude B in the z-direction and an electric field E in the x-direction. (a) Find the Lagrangian in a form where there is an ignorable coordinate. (b) Find the energy function. Is it energy? Is it conserved? Explain why. (c) Find and solve the equations of motion.
2.53A charged particle of mass m and positive charge q moves in uniform electric and magnetic fields. E and B, both pointing in the z direction. The net force on the particle is F = q (E + v x B). Write down the equation of motion for the particle and resolve it into its three components. Solve the equations and describe the particle's motion.
Consider a charged particle of mass m and positive charge Q, which moves in the presence of a uniform magnetic field, and a uniform E-field, both of which point along the positive z-axis. At t=0, the particle is at the origin: x=y=z=0. (a) Suppose that at t=0, v is 0. Describe the subsequent motion of the charged particle both quantitatively and qualitatively. (b) Now suppose that at t=0, v is non-zero and directed along positive x. Again, describe the subsequent...
A particle with charge q and mass m moves in a horizontal plane at right angles to a uniform vertical magnetic field B. a) Compute the path radius if the particle is an electron with a speed of 1.0×105 m/s traveling in a region where the field strength is 0.10 mT . answer in mm b) What is the cyclotron frequency? answer in MHz
3. (a) Show that when a particle with mass m and charge q enters a magnetic field having its velocity v perpendicular to the direction of the magnetic field B, it will perform a mv circular path of radius R- qB (b) Using the previous result find an expression for the period T of the circular motion. (c) A charged particle moves into a region of uniform magnetic field, goes through half a circle and then exits that region, as...
A proton of mass m and charge q is in both a uniform electric field, and a uniform magnetic field . Write down the three Cartesian components of the Lorentz force law and solve for the motion of the proton We were unable to transcribe this imageWe were unable to transcribe this image
3.1. You are observing the motion of a particle of charge 2.8 nC, travelling in a uniform magnetic field of unknown magnitude and direction. By analysing the motion of the charge, you determine that When the particle is travelling at a speed of 6.8 m/s in the +, direction, it experiences a force of 5.44 mN in the +0 direction; When later it is observed to be moving in the +z direction at 3.2 m/s, the force it...
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...
3. The Hamiltonian of a particle of mass m and charge q in a static magnetic field may be written 2 where πί Pi-qAi(x). We shall assume that the magnetic field B is uniform, so that AiEijkBjxk is a suitable choice. (a) Find Hamilton's equation of motion for the particle. (Hint: To simplify the algebra, use the chain rule to write9and similarly for p) 8H UT, 0z,, and similarly for Sp use the chain rule to write oz (b) Show...