Basic Theoretical Physics: A Concise Overview P13. 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. | 120 17 Electrostatics and Magnetostatics where 7 is the gravitational constant is otherwise similar to Coulomb s law in electrostatics. For a distribution of point charges the electric field E r generated by this ensemble of charges can be calculated according to the principle of superposition qk ri rk _ F 1 2 3 . qi E ri qi y 3--------i------- 3 17-5 C rk 3 tv-2 3 . This principle which also applies for Newton s gravitational forces is often erroneously assumed to be self-evident. However for other forces such as those generated by nuclear interactions it does not apply at all. Its validity in electrodynamics is attributable to the fact that Maxwell s equations are linear . the fields E and B and to the charges and currents which generate them. On the other hand the equations of chromodynamics a theory which is formally rather similar to Maxwell s electrodynamics but describing nuclear forces are non-linear so the principle of superposition is not valid there. Integral for Calculating the Electric Field For a continuous distribution of charges one may smear the discrete pointcharges qk p rk AVk and the so-called Riemann sum in equation becomes the following integral E r iiidV Q r r r 17 6 E r JJJ 4neo r r 3 This integral appears to have a singularity x lr r l-2 but this singularity is only an apparent one since in spherical coordinates near r1 r one has dV x rz r12d r r The electric field E r is thus necessarily continuous if p r is continuous it can even be shown that under this condition the field E r is necessarily continuously differentiable if the region of integration is bounded1. It can then be shown that divE r p r eo This is the first of Maxwell s equations often referred to as Gauss s law. A proof of this law is outlined below. This law is not only valid under static conditions but also quite generally . even if all quantities depend explicitly on time. 1 This is plausible since for d 1 the integral of a continuous function
