By Paul Arthur Schilpp

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The vector D is generally called the electric induction. Maxwell called it electrical displacement because of the analogy suggested by the theory of elasticity: in an elastic medium, the force E' and the displacement D' are indeed linked by a relation of type (1-67), e being the inverse of the coefficient of elasticity. So we obtain from relation (1-66) (1-70) that is (1-71) diveE = 4np av = an dive - - 4np . We will thus have, by comparing (I-50), (I-53) and (1-21) 1) the expression of the potential as a function of the charges.

PROBLEMS 1. We consider a continuous distribution of charge having spherical symmetry. Calculate the density per) that would produce the potential 1 qe- ar V= - - - eo r (a and q being constants). Calculate the charge that a point-mass at the center would have in order to produce this same potential. 2. Calculate the electrical field created by a dipole. 3. a) Calculate the electrical field El existing inside a sphere formed by a homogeneous dielectric and immersed in a constant electrical field Eo.

Solution: a) We adopt, for the external potential, a solution V of the form (I-54), and we choose three constants a, band Gl so that the following 31 ELECTROMAGNETIC THEOR Y conditions are satisfied: Eo = _ (OV) ; OZ 00 equality of the potentials equality of the normal components of the inductions oV or oV or SO-=Sl-' b) The limiting cases correspond to c) One has recourse to me = qd = sob d) So must be changed to S1> and vice-versa. The field E1 inside the cavity is included between Eo and (sdso)Eo.