An Introduction to Electrodynamics Quotes

“naturally think in vectors. They know nothing of their formal manipulation, but if they think about vectors, they think of them as vectors, that is, directed magnitudes. No ignorant man could or would think about the three components of a vector separately, and disconnected from one another. That is a devise of learned mathematicians, to enable them to evade vectors. The device is often useful, especially for calculating purposes, but for general purposes”
― Peter A. Davidson, An Introduction to Electrodynamics

“effects”
― Peter A. Davidson, An Introduction to Electrodynamics

“electrical conductivity of the solid and μ its permeability. On the other hand, the propagation of many (but certainly not all) types of waves is governed by the so-called wave equation. For example, small-amplitude”
― Peter A. Davidson, An Introduction to Electrodynamics

“average electric field in a spherical control volume | 119 R θ x′ x Figure 5.9 Geometry used to evaluate the surface integral in (5.41). and hence ¿ SR dS |x − x | = żπ 0 (2πRsinθ)(cos θ x/ x )(R dθ) (Rcos θ − |x |)2 + (Rsinθ)2 = 2πR2 x |x | ż 1 −1 χ dχ R2 + |x | 2 − 2R|x |χ , (5.42) where χ = cos θ. The integral on the second line of (5.42) may now be evaluated using the indefinite integral ż χ dχ √a − bχ = 2 b2 a − bχ 3 − a a − bχ, and after a little work we obtain ¿ SR dS |x − x | = ⎧ ⎨ ⎩ 4π 3 x, x < R, (5.43a) 4π 3 R3 |x| 3 x, x > R. (5.43b) Thus our integral of E over VR becomes ż VR E(x)dx = VR 4πε0 ż |x|>R ρe(x) (−x) |x | 3 dx − 1 3ε0 ż VR x ρe(x )dx, (5.44) or equivalently ż VR E(x)dx = VREqout(0) − pqin 3ε0. (5.45) We have arrived back at (5.39), albeit after a great deal of integration. Although this particular derivation of (5.39) is rather long-winded, some ofthe results we have deduced on route, such as (5.43a, b), will prove useful when it comesto our discussion of magnetostatics.”
― Peter A. Davidson, An Introduction to Electrodynamics