tailieunhanh - Electromagnetic Field Theory: A Problem Solving Approach Part 35

Electromagnetic Field Theory: A Problem Solving Approach Part 35. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Forces on Moving Charges 315 Moving charges over a line surface or volume respectively constitute line surface and volume currents as in Figure 5-2 where 2 becomes PfV xBdV JxBdV J pfv volume current density df ay v x B dS K x B dS K TfN surface current density 3 dl I dl ev dt ldl B Ft KdS dt KdSxB df JdVxB Figure 5-2 Moving line surface and volume charge distributions constitute currents a In metallic wires the net charge is zero since there are equal amounts of negative and positive charges so that the Coulombic force is zero. Since the positive charge is essentially stationary only the moving electrons contribute to the line current in the direction opposite to their motion ft Surface current c Volume current. 316 The Magnetic Field The total magnetic force on a current distribution is then obtained by integrating 3 over the total volume surface or contour containing the current. If there is a net charge with its associated electric field E the total force densities include the Coulombic contribution f i E vXB Newton FL A E vxB AzE IxB N m o 4 F oz E vXB ozE KxB N m2 Fv pz E vXB pzE jxB N m3 In many cases the net charge in a system is very small so that the Coulombic force is negligible. This is often true for conduction in metal wires. A net current still flows because of the difference in velocities of each charge carrier. Unlike the electric field the magnetic field cannot change the kinetic energy of a moving charge as the force is perpendicular to the velocity. It can alter the charge s trajectory but not its velocity magnitude. 5-1-2 Charge Motions in a Uniform Magnetic Field The three components of Newton s law for a charge q of mass m moving through a uniform magnetic field Bziz are dvx m qv1Bt at dVy m qvxBt dt dvz m O vl- const dt dv m vxB at 5 The velocity component along the magnetic field is unaffected. Solving the first equation for v and substituting the result into the second equation gives us a single equation in vx d vx 2 A 1 qBt 2- movx 0 v .