* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Sample Questions Q.1 : Consider two inertial reference frames S
Speed of gravity wikipedia , lookup
Classical mechanics wikipedia , lookup
Nordström's theory of gravitation wikipedia , lookup
Equations of motion wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Work (physics) wikipedia , lookup
Woodward effect wikipedia , lookup
Accretion disk wikipedia , lookup
Electromagnet wikipedia , lookup
Electromagnetism wikipedia , lookup
Superconductivity wikipedia , lookup
Maxwell's equations wikipedia , lookup
Magnetic monopole wikipedia , lookup
Special relativity wikipedia , lookup
Field (physics) wikipedia , lookup
Centripetal force wikipedia , lookup
Mathematical formulation of the Standard Model wikipedia , lookup
Electrostatics wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Metric tensor wikipedia , lookup
Time in physics wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Sample Questions 0 0 Q.1 : Consider two inertial reference frames S and S , where S is moving with constant speed v along the positive x-direction relative to S. Now imagine an observer in S sees a (electrically charged) particle of rest mass m and charge q, start from rest at the origin of S and accelerate uniformly with acceleration a in the positive y-direction. Find the velocity vector and acceleration 0 vector of the same particle as seen from S . Find the rate of change of momentum (vector) of the 0 particle in both S and S . Q.2 It is given that the particle in reference frame S in Q.1 is accelerating because there is a uniform electric field in the positive y direction (and no magnetic field). Find the magnitude of that 0 electric field. What fields do an observer in S see ? Calculate all the components of both electric 0 and magnetic fields as seen from S . Explicitly verify both the relations, d ~ + ~v × B) ~ p~ = q(E dt in reference frame S and d 0 ~ 0 + ~v 0 × B ~ 0) ~ = q(E 0p dt 0 in reference frame S . Q.3 Show that the energy momentum tensor T 0µ transforms as a contra-variant four-vector using the formula of T 0µ in terms of the electric and magnetic fields only . That means knowing how the electric and magnetic fields transform under Lorentz transformation and knowing the relation between T 0µ in terms of electric and magnetic fields show that T 0µ is a four-vector. Q.4 Find ds2 in terms of appropriate parametric variables (such as θ, φ) on the following two dimensional surfaces. (a) Torus of smaller radius a and bigger radius b. 2 2 (b) Ellipsoid of revolution obtained by rotating the ellipse xa2 + yb2 = 1 about the x-axis. Q.5 : Consider a two dimensional surface described by the metric : ds2 = (du2 + u2 dv 2 ) Cosh(2v) + 2u Sinh(2v) dudv here Cosh(x) = (ex + e−x )/2 and Sinh(x) = (ex − e−x )/2. Find the metric tensor gµν (u, v) and g µν (u, v) (choose x1 = u and x2 = v). Find the connection coefficients Γµνσ (u, v). From this find the equation of the geodesic. Find the components of the Riemann curvature tensor. What can you say about the nature of this surface ?