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For anelectron that is at rest in a uniform magnetic field B- Boe, the hamiltonian is...
Problem 7.49 A hydrogen atom is placed in a uniform magnetic field Bo Bo (the Hamiltonian can be ...
Problem 7.49
Problem 7.49 A hydrogen atom is placed in a uniform magnetic field Bo Bo (the Hamiltonian can be written as in Equation 4.230). Use the Feynman-Hellman theorem (Problem 7.38) to show that a En (7.114) where the electron's magnetic dipole moment10 (orbital plus spin) is Yo l-mechanical + γ S . μ The mechanical angular momentum is defined in Equation 4.231 a volume V and at 0 K (when they're all in the ground state) is41 Note: From...
Consider an electron in a uniform magnetic field along the z direction. A measurement shows that...
Consider an electron in a uniform magnetic field along the z direction. A measurement shows that the spin is along the negative x direction at -0. a. Find the eigenvector describing the initial spin state. 5. 0 -1 b. Write the Hamiltonian as a 2x2 matrix by starting with H =-7S-Band taking the field B in the z- direction. Find the energy eigenvalues and eigenvectors. Solve for | Ψ(t) using these eigenvalues, eigenvectors, and the initial condition from part a....
An electron enters into a uniform magnetic field directed into of the page. The magnetic field...
An electron enters into a uniform magnetic field directed into of the page. The magnetic field has a magnitude of B = 1.57. The electron will travel a semi-circle path with a radius of R=42 x 10-6 m and hits a detector. What speed did the electron have when it entered the uniform magnetic field? Electron Charge:q=1.602 x 10-19 C Electron Mass: m = 9.109 x 10-31 kg ( XB R V Detector 1.11 x 107 m/s Any electrons will...
The magnetic field over a certain range is 01.76896e-18 given by B Bi+By 3, where B...
The magnetic field over a certain range is 01.76896e-18 given by B Bi+By 3, where B 4Tand 2.4.3254e-18 3.7.209e-18 with a velocityvyv, where C4.1602-18 v 1 m/s, vy-6 m/s and v 2 m/s. O5.3.3642e-18 The charge on the electron is -1.602x 6.9.612e-19 07.1.9224e-18 08.4.005e-18 09.8.9712e-18 10.6.408e-18 By 6 T. An electron moves into the field 10-19 C What is the i component of the force ex- erted on the electron by the magnetic field? Answer in units of N Question...
Active Figure Motion of a Charged Particle in a Uniform Magnetic Field The animation below illustrates...
Active Figure Motion of a Charged Particle in a Uniform Magnetic Field The animation below illustrates a charged particle moving in circular motion due to the magnetic force caused by a constant and uniform magnetic field oriented into the page. The blue crosses represent the tails of the magnetic field vectors nstructions: Use the blue sliders to adjust the mass, speed, particle charge and magnetic field magnitude. Change each parameter and observe the eftect on the particle's motion. If the...
an electron moving perpendicular to a uniform magnetic field of 0.22 T moves in a circle...
an electron moving perpendicular to a uniform magnetic field of 0.22 T moves in a circle with a speed of 1.5×10^7 m/s. what is the radius of the circle? (e= 1.60×10^-10^-19 C, M electron =9.11×10^-31 kg)
An elctron enters a region of a uniform magnetic field with velocity v = (5.6 Times...
An elctron enters a region of a uniform magnetic field with velocity v = (5.6 Times 106 m/s) I^ +(-2.8 Times 106 m/s)j^ . If the field, B = (7.8T)^ Calculate the acceleration of the electron Calculate the radius of the electron's trajectory. Calculate the helicalthread of the electron's trajectory.
An electron has velocity V= (35i + 39j) km/s as it enters a uniform magnetic field...
An electron has velocity V= (35i + 39j) km/s as it enters a uniform magnetic field B= 70i µT. What are (a) the radius of the helical path taken by the electron and (b) the pitch of that path? (c) To an observer looking into the magnetic field region from the entrance point of the electron, does the electron spiral clockwise or counterclockwise as it moves? The charge of an electron is -1.602 × 10^-19 C and its mass is...
An electron follows a helical path in a uniform magnetic field of magnitude 0.694 T. The...
An electron follows a helical path in a uniform magnetic field of magnitude 0.694 T. The pitch of the path is 5.54 μm, and the magnitude of the magnetic force on the electron is 1.73 × 10-15N. What is the electron's speed?
An electron follows a helical path in a uniform magnetic field of magnitude 0.607 T. The...
An electron follows a helical path in a uniform magnetic field of magnitude 0.607 T. The pitch of the path is 5.57 μm, and the magnitude of the magnetic force on the electron is 2.32 × 10-15N. What is the electron's speed?
Problem 7.49
Problem 7.49 A hydrogen atom is placed in a uniform magnetic field Bo Bo (the Hamiltonian can be written as in Equation 4.230). Use the Feynman-Hellman theorem (Problem 7.38) to show that a En (7.114) where the electron's magnetic dipole moment10 (orbital plus spin) is Yo l-mechanical + γ S . μ The mechanical angular momentum is defined in Equation 4.231 a volume V and at 0 K (when they're all in the ground state) is41 Note: From...
Consider an electron in a uniform magnetic field along the z direction. A measurement shows that the spin is along the negative x direction at -0. a. Find the eigenvector describing the initial spin state. 5. 0 -1 b. Write the Hamiltonian as a 2x2 matrix by starting with H =-7S-Band taking the field B in the z- direction. Find the energy eigenvalues and eigenvectors. Solve for | Ψ(t) using these eigenvalues, eigenvectors, and the initial condition from part a....
An electron enters into a uniform magnetic field directed into of the page. The magnetic field has a magnitude of B = 1.57. The electron will travel a semi-circle path with a radius of R=42 x 10-6 m and hits a detector. What speed did the electron have when it entered the uniform magnetic field? Electron Charge:q=1.602 x 10-19 C Electron Mass: m = 9.109 x 10-31 kg ( XB R V Detector 1.11 x 107 m/s Any electrons will...
The magnetic field over a certain range is 01.76896e-18 given by B Bi+By 3, where B 4Tand 2.4.3254e-18 3.7.209e-18 with a velocityvyv, where C4.1602-18 v 1 m/s, vy-6 m/s and v 2 m/s. O5.3.3642e-18 The charge on the electron is -1.602x 6.9.612e-19 07.1.9224e-18 08.4.005e-18 09.8.9712e-18 10.6.408e-18 By 6 T. An electron moves into the field 10-19 C What is the i component of the force ex- erted on the electron by the magnetic field? Answer in units of N Question...
Active Figure Motion of a Charged Particle in a Uniform Magnetic Field The animation below illustrates a charged particle moving in circular motion due to the magnetic force caused by a constant and uniform magnetic field oriented into the page. The blue crosses represent the tails of the magnetic field vectors nstructions: Use the blue sliders to adjust the mass, speed, particle charge and magnetic field magnitude. Change each parameter and observe the eftect on the particle's motion. If the...
An elctron enters a region of a uniform magnetic field with velocity v = (5.6 Times 106 m/s) I^ +(-2.8 Times 106 m/s)j^ . If the field, B = (7.8T)^ Calculate the acceleration of the electron Calculate the radius of the electron's trajectory. Calculate the helicalthread of the electron's trajectory.
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