22-9 A point magnetic dipole moment m at rest produces a vector potential A given by 4T r3 If m moves with a constant velocity v (with v < c), show that there is also a scalar potential that a...
An ideal magnetic dipole moment m is located at the origin of an inertial system S that moves with a speed v in the x-direction with respect to an inertial system S. In the rest frame of the magnetic dipole, the vector potential is given by Eq. 5.85 in your book, 4. 12 o mxf A = - 4 r2 and the scalar potential is zero. Show that the scalar potential in the frame S is given by (1 -...
A bar magnet whosa dipole moment is (o, O, 7) A-m2 has a constant velocity of (O, O, 9) m/s. When the center of the magnet is at location (1, 7, 6) m, what is the (vector) electric field at location (1.08, 7, 3) m? N/C A bar magnet whosa dipole moment is (o, O, 7) A-m2 has a constant velocity of (O, O, 9) m/s. When the center of the magnet is at location (1, 7, 6) m, what...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one end of a string with length 1 and can swing in any direction. In fact, it moves on a sphere, a subspace of R3 1 0 φ g 2.1 Use the spherical coordinates (1,0,) to derive the Lagrangian L(0,0,0,0) = T-U, namely the difference of kinetic energy T and potential energy U. (Note r = 1 is fixed.) 2.2 Calculate the Euler-Lagrange equations, namely...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...