Consider a simple hydrogen atom where an electron orbits around a proton. Suppose a small magnetic field is applied perpendicularly to the plane of orbit. Show that if the orbit radius does not change, then the angular velocity of the electron would change by eB 2m Δω = ΕΞ

Consider a simple hydrogen atom where an electron orbits around a proton. Suppose a small magnetic field is applied perpendicularly to the plane of orbit. Show that if the orbit radius does not change, then the angular velocity of the electron would change by eB 2m Δω = ΕΞ

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A magnetic dipole moment of m = (7.50, -8.38, 4.59) Am² is inside a uniform magnetic field of B = (3.34, -6.77, 6.79) T. What is the potential energy of the dipole? (a) What is the angle between the magnetic dipole moment vector and the magnetic field vector? (b) What is the magnitude of the torque acting on the dipole?
How the Biot-Savart Law Differs from Ampère's Law A current Io flows up the z-axis from z = z, to z = 22 as shown below. %3D Z2 (a) Use the Biot-Savart law to show that the magnetic field in the z = 0 plane is Ho lo {cos 02 – cos 01}6. 4π ρ B(p, 6, 0) = |
A uniform magnetic field of 2.00×10^(−3) T is applied to put an electron into a circular orbit with angular momentum 5.00×10^(−25) kg m^2/s. Calculate the orbital radius and the speed of the electron.
Which of the following integrals will correctly solve for the force a conductor carrying a 3.1-A current directed from (2, -3, 4) m to (2, 5, 4) m experiences due to a magnetic field B = (x − y²)ax + y(x² − 1)ay + (1 − x²z)ą₂ T? O -3.1, ((2)² - 1) dy O -3.1 J [(2 + yaz + (1 – (224) ] o O The answer cannot be found on the other choices. O −3.1ƒ[(2 — ‚²³)az − (1 − (2)²(4))ax] dy - -
A sphere of radius R and mass M has a uniform volume charge density p. The sphere rotates as a rigid object with angular speed about an axis through its center. A) What is the angular momentum of the sphere about this axis? B) What is the magnetic moment of the sphere?
A charge q is distributed uniformly around a thin ring of radius r.The ring is rotating about an axis through its center and perpendicular to its plane, at an angular speed v. (a) Show that the magnetic moment due to the rotating charge has magnitude m mw 1/2 qvr 2 . (b) What is the direction of this magnetic moment if the charge is positive?
An electron is accelerated from rest through a potential difference V after which it enters a region having a magnetic field of magnitude B and direction perpendicular to the electron's velocity. The radius of the electron orbit in this magnetic field is given by: meV 2BN e 2m, V Be 2m. VB O 1 2m.V B e O 1 meV BV 2e O there is not enough information to determine 2m.V BV O none of these
An electron of kinetic energy 1.74 keV circles in a plane perpendicular to a uniform magnetic field. The orbit radius is 31.2 cm. Find (a) the electron's speed, (b) the magnetic field magnitude, (c) the circling frequency, and (d) the period of the motion. (a) Number i Units (b) Number i Units (c) Number i Units (d) Number i Units
In the Bohr model for the hydrogen atom, the electron must travel in a circular orbit of radius 5.3 x 10-11 m. Calculate the current and magnetic moment associated with this electron. Given that the magnetic field strength is in a magnitude of 9.9 x 106 A/m.
If an electron in an atom has an orbital angular momentum with m₁ = 4, what are the components (a) Lorb,z and (b) µorb,z? If the atom is in an external magnetic field that has magnitude 33 mT and is directed along the z axis, what are (c) the potential energy Uorb associated with the electron's orbital magnetic dipole moment and (d) the magnitude of the potential energy Uspin associated with the electron's spin magnetic dipole moment? If, instead, the electron has m₁ = -2, what are (e) Lorb,z, (f) Horb,z, (g) the potential energy orb associated with the electron's orbital magnetic dipole moment and (h) the magnitude of the potential energy Uspin associated with the electron's spin magnetic dipole moment? (a) Number Units (b) Number Units (c) Number i Units (d) Number Units (e) Number i Units (f) Number امل Number Hi Units Units > >
In Fig.96, the hollow conducting hemisphere of radius R=10 cm, uniform surface charge density σ = 8 × 10-⁹ C/m², which rotates around its axis of symmetry with a constant angular speed of w = 100 rad/s, a spherical segment has been removed, limited by the angle 0-45°. Find the magnetic energy of interaction between the cut hemisphere and the particle of interior magnetic moment "u" that is located on the axis at a distance d=10 cm from 0. Ομ d ...... Fig.96 R
An electron that has velocity т i = (2.0 x 106)i+ (3.0 × 106 10", %3D moves through the uniform magnetic field B = (0.030 T)î – (0.15T)f. (a) Find the force on the electron due to the magnetic field. (b) Repeat your calculation for a proton having the same velocity.