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Robert Recorde (c.1512-1558)Welsh physician and mathematician…
https://www.maths.cam.ac.uk/undergrad/admissions/files/history.pdf17 Jun 2019: James Maxwell (1831–1879) Mathematician who carried out revolutionary work on electricity and magnetism and on the kinetic theory of gases. ... Formulated ‘Maxwell’s Equations’, a major breakthrough in the field of electrodynamics. -
MATHEMATICAL TRIPOS Part III Tuesday 8 June, 2004 9 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2004/Paper51.pdf30 Aug 2019: rise to solutions of anti–self–dual (ASD) Maxwell equations on MC.Consider a covering of PT by two open sets, and show that the ASD Maxwell potentialcorresponding to the patching -
NATURAL SCIENCES TRIPOS Part IA Wednesday, 12 June, 2013 ...
https://www.maths.cam.ac.uk/undergradnst/files/2013/PaperNST_IA_2.pdf17 Jun 2019: Given that dU is an exact differential, deduce the (Maxwell)relation. (. T. V. ). S. = (. P. S. ). V. [3]. ... 9]. (b) Use the first law of thermodynamics as quoted above and Maxwell relations to provethat. (. -
If you have anything you would like to be ...
https://www.maths.cam.ac.uk/internal/files/faculty-bulletins/Issue_47-08May2018.pdf26 Nov 2019: Writing a business plan: a guide for University of Cambridge postdocs Wednesday 16th May, 5.30pm - 7.30pm, (refreshments provided), Rayleigh Seminar Room, Maxwell Centre, JJ Thomson Avenue Details of this -
MATHEMATICAL TRIPOS Part III Tuesday 5 June 2001 9 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2001/Paper49.pdf30 Aug 2019: Find µ̂(ω) for a Maxwell fluid such that. G(s) = G0es/τ. ... A Maxwell fluid of density ρ occupies a channel between the fixed planes y = h. -
MATHEMATICAL TRIPOS Part IB Wednesday 6 June 2007 1.30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2007/PaperIB_2.pdf17 Jun 2019: Show, using Maxwell’s equations, that when a steadycurrent I flows along the wire the current density within the wire is uniform. ... 17E Electromagnetism. If S is a fixed surface enclosing a volume V , use Maxwell’s equations to show that. -
NATURAL SCIENCES TRIPOS Part IB & II (General) Friday ...
https://www.maths.cam.ac.uk/undergradnst/files/2006/PaperNST_IB_2.pdf17 Jun 2019: Use suffix notation to show:. ( v) = ( v) 2v (). In the absence of charges and currents, Maxwell’s equations for an electric field Eand a magnetic field B are given by:. -
MATHEMATICAL TRIPOS Part III Monday 12 June, 2006 1.30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2006/Paper80.pdf30 Aug 2019: Use this to deduce the Maxwell approximation. a = a0 3pa0(a1 a0). ... i=1 Λi (p2/(3a0))I.From this show that the Maxwell approximation is consistent with the approximation in(iii). -
MATHEMATICAL TRIPOS Part IB Tuesday, 6 June, 2017 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2017/paperib_1_0.pdf17 Jun 2019: Part IB, Paper 1 [TURN OVER. 10. 16C ElectromagnetismWrite down Maxwell’s equations for the electric field E(x, t) and the magnetic field. ... Derive the dispersion relation that relates the angular frequency ω of the wave tothe wavevector k, and give -
NATURAL SCIENCES TRIPOS Part IB Friday, 1 June, 2018 ...
https://www.maths.cam.ac.uk/undergradnst/files/2018/papernst_ib_2_2018.pdf17 Jun 2019: b) Maxwell’s equations for the electric and magnetic fields E(x, t) and B(x, t) in a vacuumcan be written as. -
MATHEMATICAL TRIPOS Part IB Wednesday, 8 June, 2011 1:30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2011/PaperIB_2.pdf17 Jun 2019: Find expressions for E and B in terms of A and show that Maxwell’sequations are all satisfied provided A satisfies the appropriate Poisson equation. ... Show using the relevant Maxwell equationthat the magnetic field B inside the solenoid is uniform, -
MATHEMATICAL TRIPOS Part III Tuesday 10 June 2003 9 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2003/Paper53.pdf30 Aug 2019: Your essay shouldinclude a discussion of the superspace analogs of the Maxwell gauge potential, gaugetransformations, field strength and Bianchi identity. -
MATHEMATICAL TRIPOS Part IB Wednesday 7th June, 2006 1.30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2006/PaperIB_2.pdf17 Jun 2019: 6G Electromagnetism. Given that the electric field E and the current density j within a conducting mediumof uniform conductivity σ are related by j = σE, use Maxwell’s equations to show ... Derive from Maxwell’s equations the Biot-Savart law. B(r) = -
MATHEMATICAL TRIPOS Part III Tuesday 12 June 2001 9 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2001/Paper39.pdf30 Aug 2019: Discuss briefly the behaviour of the total dielectronic recombination coefficient. [You may assume that the Maxwell velocity distribution is. -
MATHEMATICAL TRIPOS Part IB Thursday 5 June 2008 9.00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2008/PaperIB_3.pdf17 Jun 2019: 10. 17B Electromagnetism. (i) From Maxwell’s equations in vacuum,. E = 0 E = Bt. ... v) Using Maxwell’s equations in vacuum prove that:A. (1/µ0)(E B) dA =. t. V. (0E. 2. 2B2. 2µ0. )dV , (1). where V is the closed volume and A -
MATHEMATICAL TRIPOS Part III Thursday, 26 May, 2016 9:00 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2016/paper_301.pdf30 Aug 2019: 3. 4. One way of quantizing the electromagnetic field is to consider a different startingpoint from the usual Maxwell action. -
MATHEMATICAL TRIPOS Part IB Thursday 9 June 2005 9 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2005/PaperIB_3.pdf17 Jun 2019: 9. 17H Electromagnetism. If E(x, t), B(x, t) are solutions of Maxwell’s equations in a region without anycharges or currents show that E′(x, t) = cB(x, t), ... n B = 0 , n E = 0. Electromagnetic waves inside a perfectly conducting tube with axis -
MATHEMATICAL TRIPOS Part III Friday, 4 June, 2010 1:30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2010/Paper54.pdf30 Aug 2019: Show that Fab = 2[aVb]satisfies Maxwell’s equations. (iii) Consider Minkowski spacetime in spherical polar coordinates (t, r, θ, φ). -
MATHEMATICAL TRIPOS Part III Thursday 31 May 2007 1.30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2007/Paper61.pdf30 Aug 2019: In electromagnetism in Minkowski spacetime the equations relating the 4-vectorpotential Aa, the Maxwell field tensor Fab and the 4-current density J a are. -
MATHEMATICAL TRIPOS Part IB Tuesday, 3 June, 2014 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2014/PaperIB_2.pdf17 Jun 2019: Determine the valueof G(0) and explain briefly how it is related to the values of f ′. 6A ElectromagnetismStarting from Maxwell’s equations, deduce that. dΦ. dt= E,. for a moving ... Using Maxwell’sequations and the divergence theorem, derive a -
MATHEMATICAL TRIPOS Part III Friday 31 May 2002 1.30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2002/Paper53.pdf30 Aug 2019: A Maxwell fluid having density ρ and relaxation modulus. G(t) = G0et/τ. -
First Year (Part IA) A brief introduction to the ...
https://www.maths.cam.ac.uk/undergrad/admissions/files/intrototripos.pdf17 Jun 2019: Maxwell’s equations. are the fundamental equations of electromagnetism; solutions tell us, for example, how light propagates. • -
If you have anything you would like to be ...
https://www.maths.cam.ac.uk/internal/files/faculty-bulletins/Issue_34-4September2017.pdf26 Nov 2019: DAMTP NEWS BULLETIN 04/09/2017. ACADEMIC NEWS. • Thomas Crawford, former PhD student, has recently posted the following articles on his webpage: Equations Stripped: Maxwell’s equations of electromagnetism; Perelman and -
PaperIB_2.dvi
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2009/PaperIB_2.pdf17 Jun 2019: Part IB, Paper 2. 9. 17A Electromagnetism. Starting from Maxwell’s equations in vacuo, show that the cartesian components ofE and B each satisfy. -
MATHEMATICAL TRIPOS Part IB Friday 9th June, 2006 1.30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2006/PaperIB_4.pdf17 Jun 2019: 7G Electromagnetism. Starting from Maxwell’s equations, deduce Faraday’s law of induction. -
MATHEMATICAL TRIPOS Part IB Wednesday, 5 June, 2013 1:30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2013/PaperIB_2.pdf17 Jun 2019: 6D ElectromagnetismUse Maxwell’s equations to obtain the equation of continuity. ρ. -
MATHEMATICAL TRIPOS Part IB Tuesday, 7 June, 2011 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2011/PaperIB_1.pdf17 Jun 2019: Part IB, Paper 1. 9. 16D ElectromagnetismStarting from the relevant Maxwell equation, derive Gauss’s law in integral form. -
MATHEMATICAL TRIPOS Part IB Thursday, 7 June, 2012 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2012/PaperIB_3.pdf17 Jun 2019: Part IB, Paper 3 [TURN OVER. 8. 17B ElectromagnetismUsing the Maxwell equations. -
MATHEMATICAL TRIPOS Part IB Thursday, 9 June, 2011 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2011/PaperIB_3.pdf17 Jun 2019: Part IB, Paper 3 [TURN OVER. 8. 17C ElectromagnetismShow, using the vacuum Maxwell equations, that for any volume V with surface S,. -
MATHEMATICAL TRIPOS Part IB Friday, 4 June, 2010 1:30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2010/PaperIB_4.pdf17 Jun 2019: Derive from Maxwell’s equations the result. E = dΦ. dt(). where the electromotive force E =C. -
MATHEMATICAL TRIPOS Part IB Tuesday, 31 May, 2016 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2016/paperib_1.pdf17 Jun 2019: Show that the value of U0 must satisfy. π22. 8ma2< U0 <. 9π22. 8ma2. Part IB, Paper 1. 9. 16D Electromagnetism(a) From the differential form of Maxwell’s equations with J = -
MATHEMATICAL TRIPOS Part IB Thursday, 6 June, 2013 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2013/PaperIB_3.pdf17 Jun 2019: Find an electric field E0 that satisfies the Maxwell equation. E = Bt. -
MATHEMATICAL TRIPOS Part IB Friday, 8 June, 2012 1:30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2012/PaperIB_4.pdf17 Jun 2019: of a single closed loop of wire. Use the Maxwell equation. -
MATHEMATICAL TRIPOS Part IB Wednesday, 6 June, 2018 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2018/paperib_2_2018.pdf17 Jun 2019: r r′|3dV. from Maxwell’s equations, where the time–independent current j(r) vanishes outside V. -
MATHEMATICAL TRIPOS Part IB 2004 List of Courses Analysis ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2004/list_IB.pdf17 Jun 2019: Part IB 2004. 31. 1/I/7B Electromagnetism. Write down Maxwell’s equations and show that they imply the conservation ofcharge. ... d. dt(XB). 3/II/19B Electromagnetism. Starting from Maxwell’s equations, derive the law of energy conservation in theform -
MATHEMATICAL TRIPOS Part IB Friday, 3 June, 2016 1:30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2016/paperib_4.pdf17 Jun 2019: 7D Electromagnetism(a) Starting from Maxwell’s equations, show that in a vacuum,. -
MATHEMATICAL TRIPOS Part IB Friday, 7 June, 2019 1:30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2019/paperib_4_2019.pdf17 Jun 2019: Calculate the expectation value of the momentum forthis wavefunction. 7A ElectromagnetismWrite down Maxwell’s Equations for electric and magnetic fields E(x, t) and B(x, t). -
MATHEMATICAL TRIPOS Part IB Thursday, 7 June, 2018 1:30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2018/paperib_3_2018.pdf17 Jun 2019: E > 12ω. 17C ElectromagnetismUse Maxwell’s equations to show that. d. -
MATHEMATICAL TRIPOS Part IB Friday, 8 June, 2018 1:30pm ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2018/paperib_4_2018.pdf17 Jun 2019: Part IB, Paper 4 [TURN OVER. 4. 7C ElectromagnetismShow that Maxwell’s equations imply the conservation of charge. -
MATHEMATICAL TRIPOS Part IB Friday, 5 June, 2015 1:30 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2015/PaperIB_4.pdf17 Jun 2019: 4. 7A ElectromagnetismFrom Maxwell’s equations, derive the Biot–Savart law. B(r) =µ04π. -
MATHEMATICAL TRIPOS Part IB 2010 List of Courses Analysis ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2010/PaperIB_all.pdf17 Jun 2019: Derive from Maxwell’s equations the result. E = dΦdt. (). where the electromotive force E =C q. ... Write down Maxwell’s equations in terms of e, b, k and ω. -
MATHEMATICAL TRIPOS Part II Friday, 7 June, 2019 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2019/paperii_4_2019.pdf16 Oct 2019: D = εE, B = µH. Write down Maxwell’s equations for E, B, D and H in the absence of free charges andcurrents. ... By constructing a correspondingsolution of Maxwell’s equations, derive the law of reflection θI = θR and Snell’s law ofrefraction, -
MATHEMATICAL TRIPOS Part II Friday 8 June 2007 9 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2007/PaperII_4.pdf17 Jun 2019: Obtain Maxwell’s equations in 4-vector form. Another action that is sometimes suggested is. ... Ŝ[Aa] =. d4x. {1. 2µ0Aa,bAa,b JaAa. }. Under which additional assumption can Maxwell’s equations be obtained using this action? -
MATHEMATICAL TRIPOS Part III Friday 10 June, 2005 1.30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2005/Paper55.pdf30 Aug 2019: 3 Starting with the Maxwell action in five dimensions, explain how this can give riseto an infinite number of states in four dimensions after compactifying on a circle of radiusr. -
MATHEMATICAL TRIPOS Part II Alternative A Thursday 5 June ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2003/PaperIIA_3.pdf17 Jun 2019: E(r, t) =(0,x/t2, 0. ),. use the Maxwell equation. E = Bt. ... Hence show, using (1) andStokes’ theorem, that (2) is a consequence of Maxwell’s equations. -
MATHEMATICAL TRIPOS Part IB 2005 List of Courses Linear ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2005/list_IB.pdf17 Jun 2019: 53. 2/I/6H Electromagnetism. Write down Maxwell’s equations in the presence of a charge density ρ and currentdensity J. ... Part IB 2005. 26. 3/II/17H Electromagnetism. If E(x, t), B(x, t) are solutions of Maxwell’s equations in a region without -
MATHEMATICAL TRIPOS Part II Alternative A Wednesday 4 June ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2003/PaperIIA_2.pdf17 Jun 2019: Write down the vacuum Maxwell equations and show that they imply. -
MATHEMATICAL TRIPOS Part II Alternative A Thursday 7 June ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2001/PaperIIA_4.pdf17 Jun 2019: Use two of Maxwell’s equations to prove thatC. (E v B) dr = ddt. -
MATHEMATICAL TRIPOS Part III Friday 28 May, 2004 1.30 ...
https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2004/Paper46.pdf30 Aug 2019: c) The Maxwell construction, the occurrence of domains and the phenomenon ofhysteresis;. -
MATHEMATICAL TRIPOS Part IB Thursday, 3 June, 2010 9:00 ...
https://www.maths.cam.ac.uk/undergrad/pastpapers/files/2010/PaperIB_3.pdf17 Jun 2019: 10. 17C Electromagnetism. Write down Maxwell’s equations in a region with no charges and no currents.Show that if E(x, t) and B(x, t) is a solution then ... Write down Maxwell’s equations in terms of e, b, k and ω.
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