Transcript Slide 1
Today’s agenda: Magnetic Fields. You must understand the similarities and differences between electric fields and field lines, and magnetic fields and field lines. Magnetic Force on Moving Charged Particles. You must be able to calculate the magnetic force on moving charged particles. Magnetic Flux and Gauss’ Law for Magnetism. You must be able to calculate magnetic flux and recognize the consequences of Gauss’ Law for Magnetism. Motion of a Charged Particle in a Uniform Magnetic Field. You must be able to calculate the trajectory and energy of a charged particle moving in a uniform magnetic field. Motion of a charged particle in a uniform magnetic field Example: an electron travels at 2x107 m/s in a plane perpendicular to a 0.01 T magnetic field. Describe its path. Example: an electron travels at 2x107 m/s in a plane perpendicular to a 0.01 T magnetic field. Describe its path. The force on the electron (remember, its charge is -) is always perpendicular to the velocity. If v and B are constant, then F remains constant (in magnitude). The above paragraph is a description of uniform circular motion. B v F F - v The electron will move in a circular path with a constant speed and acceleration = v2/r, where r is the radius of the circle. Motion of a proton in a uniform magnetic field v Bout FB r v + + FB FB v + The force is always in the radial direction and has a magnitude qvB. For circular motion, a = v2/r so mv 2 F = q vB = r v= q rB m mv r= qB Thanks to Dr. Waddill for the use of the picture and following examples. The period T is 2πr 2πm T= = v qB The rotational frequency f is called the cyclotron frequency qB 1 f= = T 2πm Remember: you can do the directions “by hand” and calculate using magnitudes only. Helical motion in a uniform magnetic field If v and B are perpendicular, a charged particle travels in a circular path. v remains constant but the direction of v constantly changes. If v has a component parallel to B, then v remains constant, and the charged particle moves in a helical path. There won’t be any test problems on helical motion. B v + v Apply B-field perpendicular Electrons confined to move to in aplane plane Thanks to Dr. Yew San Hor for this and the next slide. Apply B-field perpendicular to plane Lorentz Force Law If both electric and magnetic fields are present, F = q E+ v B . Applications See your textbook for numerical calculations related the next two slides. If I have time, I will show the mass spectrometer today. The energy calculation in the mass spectrometer example is often useful in homework.