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3. A particle of mass m, charge q, and inital velocity vo is injected into uniform...
The equations of motion for a particle of mass m and electrical charge q under the...
The equations of motion for a particle of mass m and electrical charge q under the influence of a uniform magnetic field B perpendicular to the plane of motion are mx" = qBy' and my" = -qBx'. where x and y are the horizontal Cartesian position coordinates of the particle. Suppose that the particle initially satisfies the conditions Solve the initial value problem and sketch out the trajectory of the particle for t Greaterthanorequalto 0.
2.53A charged particle of mass m and positive charge q moves in uniform electric and magnetic...
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.
Find the law of motion of a particle mass m and zero energy in one dimension...
Find the law of motion of a particle mass m and zero energy in
one dimension in the field U(x) = -Ax^(4) where A is a positive
constant. Given the inital position x0, compute how much time does
it take for the particle to escape to infinity if the vector of
initial velocity of the particle is pointing away from the origin
x=0. Describe the motion when the vector of inital velocity of the
particle is pointing toward x=0.
3....
3. A particle with mass m and charge q moves in a uniform magnetic filed of...
3. A particle with mass m and charge q moves in a uniform magnetic filed of magnitude B that is oriented along the z axis. (a) Neglecting the effects of spin and using the so-called Landau gauge with the vector po- tential given by A = (-By,0,0), show that the Hamiltonian may be written as À = 2m 2 ++øp +29BD2y +(, 2] (1) с (b) Because Pa and Êz commute with Ĥ, the time-independent Schrödinger equation for (x, y,...
A particle with charge q exists in a region with a uniform electric field Ē =...
A particle with charge q exists in a region with a uniform electric field Ē = Eî. There is no magnetic field. The particle’s initial velocity is ū = voĉ. The initial position is at the origin. a. Write the differential equation of motion using Newton's second law. Write it in vector form, and then write an equation for each component. b. Find x(t), y(t), and z(t).
A charged particle with mass M and charge q moves in the x – y plane....
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.
A particle with positive charge q = 1.12 10-18 C moves with a velocity v with...
A particle with positive charge q = 1.12 10-18 C moves with a velocity v with arrow = (5î + 2ĵ − k) m/s through a region where both a uniform magnetic field and a uniform electric field exist. (a) Calculate the total force on the moving particle, taking B with arrow = (5î + 2ĵ + k) T and E with arrow = (2î − ĵ − 4k) V/m. (b) What angle does the force vector make with the...
Consider a charged particle of mass m and positive charge Q, which moves in the presence...
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 of mass m is in a potential energy field described by, V(x, y) =...
A particle of mass m is in a potential energy field described by, V(x, y) = 18kx² +8ky? where k is a positive constant. Initially the particle is resting at the origin (0,0). At time t = 0 the particle receives a kick that imparts to it an initial velocity (vo, 2vo). (a) Find the position of the particle as a function of time, x(t) and y(t). (b) Plot the trajectory for this motion (Lissajous figure) using Vo = 1,...
5. A small particle of velocity vo-8.1 × 103 m/s asit enters a region of uniform...
5. A small particle of velocity vo-8.1 × 103 m/s asit enters a region of uniform magretic field. The particle is observed to travel in the semicircular path with radius R 5.0 cm. Cakculate the (a) magnitude and (b) direction of the magnetic fleld in the region charge q-1,9 x 10-6 C and mass m "3.1x10-12kg has
The equations of motion for a particle of mass m and electrical charge q under the influence of a uniform magnetic field B perpendicular to the plane of motion are mx" = qBy' and my" = -qBx'. where x and y are the horizontal Cartesian position coordinates of the particle. Suppose that the particle initially satisfies the conditions Solve the initial value problem and sketch out the trajectory of the particle for t Greaterthanorequalto 0.
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.
Find the law of motion of a particle mass m and zero energy in
one dimension in the field U(x) = -Ax^(4) where A is a positive
constant. Given the inital position x0, compute how much time does
it take for the particle to escape to infinity if the vector of
initial velocity of the particle is pointing away from the origin
x=0. Describe the motion when the vector of inital velocity of the
particle is pointing toward x=0.
3....
3. A particle with mass m and charge q moves in a uniform magnetic filed of magnitude B that is oriented along the z axis. (a) Neglecting the effects of spin and using the so-called Landau gauge with the vector po- tential given by A = (-By,0,0), show that the Hamiltonian may be written as À = 2m 2 ++øp +29BD2y +(, 2] (1) с (b) Because Pa and Êz commute with Ĥ, the time-independent Schrödinger equation for (x, y,...
A particle with charge q exists in a region with a uniform electric field Ē = Eî. There is no magnetic field. The particle’s initial velocity is ū = voĉ. The initial position is at the origin. a. Write the differential equation of motion using Newton's second law. Write it in vector form, and then write an equation for each component. b. Find x(t), y(t), and z(t).
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.
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 of mass m is in a potential energy field described by, V(x, y) = 18kx² +8ky? where k is a positive constant. Initially the particle is resting at the origin (0,0). At time t = 0 the particle receives a kick that imparts to it an initial velocity (vo, 2vo). (a) Find the position of the particle as a function of time, x(t) and y(t). (b) Plot the trajectory for this motion (Lissajous figure) using Vo = 1,...
5. A small particle of velocity vo-8.1 × 103 m/s asit enters a region of uniform magretic field. The particle is observed to travel in the semicircular path with radius R 5.0 cm. Cakculate the (a) magnitude and (b) direction of the magnetic fleld in the region charge q-1,9 x 10-6 C and mass m "3.1x10-12kg has
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