Basic Theoretical Physics: A Concise Overview P15. This concise treatment embraces, in four parts, all the main aspects of theoretical physics (I . Mechanics and Basic Relativity, II. Electrodynamics and Aspects of Optics, III. Non-relativistic Quantum Mechanics, IV. Thermodynamics and Statistical Physics). It summarizes the material that every graduate student, physicist working in industry, or physics teacher should master during his or her degree course. It thus serves both as an excellent revision and preparation tool, and as a convenient reference source, covering the whole of theoretical physics. It may also be successfully employed to deepen its readers’ insight and. | 140 17 Electrostatics and Magnetostatics one obtains divB 0 or better dVd2A B n 0 W Maxwell II . there are no true magnetic charges at all but only magnetic dipoles. The above relation is the second Maxwell equation which is again essentially based on experimental experience. Using these relations the magnetic field H in the absence of electric currents can be derived from a magnetic potential fm which is calculated from equations analogous to and . The reader - if a student undergoing examinations - should write down the equations as preparation for a possible question. Solution H r -grad m r with the two equivalent formulae a dipole representation for magnetized bodies r I L dy J rQ r - r 4np0 r r 3 b representation in terms of effective magnetic charges tm r fjf d divJ r 4np 0 r r d2A J r n r dG ho r r Forces and Torques on Electric and Magnetic Dipoles The force on an electric dipole in an electric field may be calculated using the dumbbell approximation of two opposite charges at slightly different positions 3 F a E r E r a a a---------------------------I E r r r a r q 2 7 V 2 q dxj J o p V E r . In the dipole limit q o œ a o 0 but q o p 0 whereas qa aj o 0 one obtains the result F p grad E r . A similar calculation yields the formula for the torque D a a r a a y -- 7 1 T I _ I Z l V I _ I _ rtr _ _ Lf I nr _ _ D q r X E i r X E i q 27 2J 27 2 o p X E r . For the magnetic case one only needs to replace p by m and E by H. Electrostatic and Magnetostatic Fields in Polarizable Matter 141 The Field Energy We shall now introduce a number of different but equivalent expressions for the energy associated with an electric field. The expressions are fundamental and will be used later. Firstly we shall start with a capacitor with dielectric material of dielectric constant between the plates. Let us transport an infinitesimal amount of charge14 8Q from the metal plate at lower potential to that with the .
