Examine the effect of symmetric T on the Hamiltonian of an e ormation g in the coulomb potentical.
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- (Pr. 4) If a soft material has a dielectric response characterized by a single relaxation time t, then the polarization - [P(t)- XoE (t)], where X is the static electric susceptibility. obeys the equation: dP dt T (a) Under an applied sinusoidal field given, in complex notation, by E(t) = Ege-iw verify by direct substitution that P = XEE e-i satisfies the equation dP(t) = − ² [P(t) = x₂ €₁E (t)]. Show that the complex - dt hence calculate the real and imaginary parts of the complex Xs 1-iw susceptibility obeys the Debye law x = susceptibility, and sketch what they look like. (c) Apply this model to the case of water at room temperature, for which Xs≈ 80 and t = 9.4 ps. Compute the frequency in Hz at which the imaginary part of the susceptibility is maximum. What is the real part of the susceptibility of water for quasistatic fields (low frequency)? And for high frequency? When is water more polarizable by the electric field, and why? Is water a Newtonian liquid at low frequency? And at…Consider an infinite hollow conducting cylinder of inner radius R and outer radius 3R, as shown. The non-uniform current density J is out of the page and varies with distance r fromthe center as J=J0rk (k is k hat) where J0 is a positive constant. Calculate the magnetic field at point P (r = 2R) from the centre,(magnitude and direction). Sketch the Amperian loop.Two magnetic systems in thermal contact Consider two isolated systems of noninteracting spins with NA = 4 and NB = 16. Their initial energies are EA = -2µB %3D %3D and Eb= -2µB. What is the most probable macrostate for the composite system?
- Please do number 8.Calculate the potential energy of the interaction between two linear quadrupoles when they are collinear and their centres are separated by a distance r.A small object with dipole moment p is released near its equilibriumorientation in a uniform electric field of magnitude E.The rotational inertia of the dipole is I. (a) What is the effectivetorsional constant k of this simple harmonic system? (b)Calculate the angular frequency v of small oscillations aboutthe equilibrium orientation.
- I need the answer as soon as possibleA particle of charge Q is located outside an infinitely long cylinder whose axis points out of the page on which is wrapped an infinitely long current-carrying wire with steady current I. If the particle is launched with speed Vo, determine the directions such that it experiences zero magnetic force. left or right in or out up or down the force is maximum any direction