EXERCISE 1.2 Show that P-Q is perpendicular to both P and Q. (Hint: Try to prove both (P × Q) • P and (P × Q) • Q are zero.)
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- φ(r, t) = Z d 3 r 0 ρ(r 0 , t) |r − r 0 | (1.4.35) In Eq. (1.4.35), the potential φ at position r is instantaneously determined by the charge density ρ at positions r 0 that are a finite distance away. Is this spooky action-at-a-distance? Does it worry you that causality seems to be violated? Information at r 0 seems to be instantly conveyed to the distant point r, even though nothing can travel faster than the speed of light.For the pipe assembly of Prob. 4.101, determine (a) the largest permissible value of a if the assembly is not to tip, (b) the corresponding tension in each wire.(Reference to Problem 4.101):Two steel pipes AB and BC , each having a mass per unit length of 8 kg/m, are welded together at B and supported by three vertical wires. Knowing that a= 0.4 m, determine the tension in each wire.Construct the 3D rotation ma- trices for rotations about the x-axis, y-axis, and z-axis by an angle o as described in I section 1.1.5. You should end up with three 3x3 matrices, one for each rotation axis. Demonstrate that your matrices do what they are supposed to do by considering >= 90 deg and applying them to an arbitrary vector A. Draw pictures to illustrate your reasoning.