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By Kronig R. L.
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Extra info for The Magnetic Moment of the Electron
Sample text
5, we find that 1 Note that the quantity All un ΘΛ„ is also numerically equal to the area of the parallelogram formed by À + />' in the x-y plane. 28 Chapter 2 Vector Analysis 2 A ■ ■ C = A* В ··(.. 5 Cross product of vectors À and В for the special case of A and В in the x—y plane. A x B = (Λ,ά, + Λ,Α,^χίβ,ά, + Byây) = (AxBy-ÀyBx)â. 17) For the more general case of vectors A and В with three components, A X В = (Л ,ά, + Ayây + AM. S. 18 may be written as a determinant in the form Axli= <"', A A,-x B, «, A A,v В (l- A.
Therefore, since dV —— * 0 and — - Ф 0 in general, V V must be perpendicular to the curve С. 16. On this surface, dV = 0, so (dV/dx)dx + (bVßy)dy + (dV/dz)dz = 0. 15 of x and y. Plol of VU. 16 An equipotential surface for a charge, q. al the origin. But we can see that, if we restrict ourselves to the iso-surface (the sphere), then dl must be on the surface of the sphere, so we conclude that V V must be orthogonal to the sphere. 1 Find a unit vector parallel to the (дг, у) plane and normal to the curve x1 - xy + y2 = 7 at the following: a.
At that time, vector algebra and matrices had not yet been developed, but the vector dot and cross product were a result of Hamilton's work. It is said that Hamilton was walking across the Royal Canal in Dublin with his wife when the solution to quaternions came to him in the form of an equation, which he inscribed in stone on the bridge now called the Brougham or Broom Bridge. 42 added for this book. 20 Chapter 1 Foundations of Maxwell's Equations number (a + ib), where a and b are real and i2 - —1.