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  • leçon - matière potentielle : inside the circle
AN ELECTROMAGNETIC ROCKET HYPER-LIGHT STELLAR DRIVE Paul A. Murad1 Vienna, Virginia 22182 ABSTRACT Virtues of electromagnetic propulsion are examined in light of recent data published about unusual vehicles. If conditionally treated as credible evidence, enough information exists to develop an electromagnetic rocket and compels reexamining Maxwell's equations indicating: o Electric surface currents exist that may sustain a force, o An analogue exists regarding electric and magnetic effects to generate axial thrust, o Maxwell's equations admit a relativistic solution, and o A cyclonic drive may represent a hyper-light electromagnetic rocket capable of accelerating particles.
  • light speeds
  • sinh sinh
  • charge density
  • ring
  • magnetic field
  • particle
  • electric field
  • velocity
  • electron



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Solutions Sheet 3, DifferentiationQuestions 19-28v2
19) Go back to the definition and forx6= 0 consider
sinx f(x)f(0)1 sinxxsinxx x = = =x . 2 3 x0xx x Thus, by the Product Rule,     f(x)f(0) sinxxsinxx lim = limx= limxlim 3 3 x0x0x0x0 x0x x   1 = 0× −= 0. 6
Since the limit exists the functionfis differentiable atx= 0 with derivative 0.
20)Chain or Composite Rule Ifgis differentiable ataandfis differentiable atg(a)thenfgis differentiable ataand
0 0 0 (fg) (a) =f(g(a))g(a).
i) By the Composite Rule, and an earlier Question,   d1 cosy1 1 tanh (siny) = cosy= =. 2 2 dy1(siny) cosycosy
This is valid as long as|siny|<1,which is certainly true fory(π/2, π/2).
ii) By the Composite Rule, and an earlier Question,   dcos1 1 y1 1 sinh (tany) =q×= =. 2 2 dy2cosycosycosy 1 + (tany)
True as long as cosy6= 0 and so certainly true fory(π/2, π/2).
iii) Recall from an earlier Question 12 that
d1 1 coshy=p dy 2 y1