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- The infinitesimal external work required to increase the overall dipole moment of a uniformly polarised dielectric substance from p to p + dp in an electric field E is SW = Edp. i. Show that the Gibbs free energy is given by dG = -SdT - pdE. Establish the Maxwell relation: ii. as (35), = (77) E The polarisation per unit volume of a dielectric substance is given by: B=C²0² Р € E where E and C are constants and V is the (constant) volume of the system. iii. Using a suitable Maxwell relation and the equation of state show that: (F) T = 0Find the value of the commutator a. 3 p O b. 1 O C. 0 O d. – 1 O 8: 3 2Chapter 37, Problem 012 The length of a spaceship is measured to be exactly 1/2 its rest length. (a) What is the speed parameter ß of the spaceship relative to the observer's frame? (b) By what integer factor do the spaceship's clocks run slow, compared to clocks in the observer's frame? (a) Number Units (b) Number Units
- A pure lead bar 10 cm long is maintained with one end at T = 300 K and the other at 310 K. The thermoelectric potential difference thus induced across the ends is 12.8 μV. Find the thermoelectric power for lead in this temperature range. (Note: Q varies nonlinearly with temperature, but over this narrow temperature range, you may use a linear approximation.)Find the gradient field F = Vo for the potential function o below. P(x,y.z) = In (3x +y° +z²) Vøxy.z) = (O Vo(x.y.z z)3DFigure 1.52 shows a spherical shell of charge, of radiusa and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise using direct integration.