Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
History of electromagnetic theory wikipedia , lookup
Circular dichroism wikipedia , lookup
Magnetic monopole wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Electrical resistivity and conductivity wikipedia , lookup
Woodward effect wikipedia , lookup
Maxwell's equations wikipedia , lookup
Lorentz force wikipedia , lookup
Superconductivity wikipedia , lookup
Electromagnet wikipedia , lookup
PHYS2012 ASSIGNMENT 2010 ELECTROMAGNETIC PROPERTIES OF MATERIALS DUE FRIDAY 15 OCT 2101 Question 1 On a macroscopic scale, when the polarization P is proportional to the electric field E within the dielectric (dielectric constant r) P=np p=qd P e o E r 1 o E where n is the number density (molecules/volume), p is the dipole moment, q is the charge separated and d is the charge separation. On an microscopic scale an induced electric dipole moment p is proportional to an external electric field E and the constant of proportionality is called the polarisability of the molecule p E For an atom (assume atom spherical volume of radius a), 4 o a 3 For non-polar molecules (no permanent electric dipole moments) For a dilute medium (r ~ 1) o ( r 1) n A better model that can be applied to more dense media, is the Clausius-Mossotti 3 1 o r equation n r 2 (a) What is a simple way to measure r? n (b) Plot vs. r (r from 1 to 1.5) for a dilute and dense media. o (c) What is the approximate value of r when the equation for the polarisability of non-polar molecules for a dilute medium fails? (d) The dielectric constant for oxygen gas is rg = 1.000523 and its molar mass is 32.0 g. One mole of oxygen gas at STP (273 K, 1 atm) has a volume of 22.4 L. In the liquid state, the density of oxygen is 1.190103 kg.m-3. (NA = 6.021023) (i) Calculate the number densities for oxygen in the gas ng and liquid nl states. (ii) Estimate the radius of an oxygen atom. Is your answer reasonable? (iii) Assume that the atomic polarizability is the same in the gaseous and liquid states. Estimate its dielectric constant for liquid oxygen r l. Comment on your answer (e) The oxygen gas was placed into an external electric field E = 12.5 kV.m-1. (i) Calculate the induced electric dipole moment p. (ii) Calculate the separation d between the centre of positive and negative charge for the oxygen atoms. Comment on your answer. 1 Question 2 A parallel plate capacitor has a square plate area of 0.200 m2 and a plate separation of 0.0100 m. The potential difference between the plates is 3.00 kV. A dielectric slab with a dielectric constant of 3 completely fills the space between the plates of the capacitor. While the capacitor is still connected to the battery, the dielectric slab is partially removed. The slab is withdrawn in a direction parallel to the plates through a distance x (slab fully inserted, x = 0 and half space filled, x = L/2, slab fully removed, x = L). Assume the dielectric slab is removed very slowly so that the kinetic energy of the slab is zero and that edge effects at the ends of the capacitor can be ignored. (a) Show and justify the following relationship as functions of x Capacitance Charge Energy stored by capacitor L C 0 x r L x d LV Q 0 x r L x d LV 2 U cap 0 x r L x 2d U cap U cap ( x) U cap (0) LV 2 U cap 0 x r L x r L 2d Change in energy stored by battery qbattery Q( x) Q(0) LV 2 U battery 0 x r L x r L d 2 LV Work done by external force Wme 0 x r L x r L 2d External force in removing dielectric LV 2 Fme 0 r 1 independent of x 2d (b) Calculate the above quantities when x = 0, L/2, L. Comment on the changes. x=0 x = L/2 x = L Comments x m x increasing -10 C 10 F Q 10-6 C Ucap 10-3 J Is energy to or from capacitor? Ucap 10-3 J -3 Is energy to or from battery? Ubattery 10 J Wme 10-3 J Fme 10-3 N 2 Question 3 A metal sphere of radius a and charge +Q is surrounded by a thick spherical layer of dielectric material with a dielectric constant r and it has an outer radius b as measured from the centre of the metal sphere. Starting with Gauss’s Law in the form D dA q f show and/or justify the following relationships inside the dielectric material (a < r < b): (a) (b) (c) (d) (e) (f) Q radial outward 4 r 2 Q Qb Q electric field E radial outward 2 4 r 0 r 4 0 r 2 electric displacement D 1 Qb Q r r Q r 1 polarization P radial outward 4 r 2 r 1 3 rˆ 3 bound charge density b Q r (r ) use 2 4 r r r Bound charge within the interior of dielectric material r 1 3 r 1 r 1 3 d Q ( r ) d Q ( r ) d Q b r r r surface charge density Q r 1 b (r a) 4 a2 r bound charge (at each surface) b (r b) Q r 1 4 b2 r (g) total charge of dielectric material Qdielectric = 0. (h) Sketch the electric field lines inside and outside the dielectric material. Explain why the number of electric field line change at the boundaries of the dielectric material. (i) Sketch the distribution of the free and bound charges for the metal sphere and dielectric material. (j) How does the electric field surrounding the metal sphere (charge +Q) and dielectric layer compare with the electric field surrounding a point charge Q? Explain. 3 Question 4 A hysteresis curve for a sample of iron is shown in the diagram below. (a) What are the important features of the hysteresis curve? Hysteresis Curve for an Iron sample 2.0 1.5 1.0 B (T) 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -100 -50 0 H 50 100 (A.m-1) (http://www.whitefang.net/Academics/Physics/I3-Hysteresis/hysteresis.htm) A Rowland ring is a donut shaped ring or torus of a given ferromagnetic material with two coils around it. The first long coil is used to set up the H-field inside the ring by a current i. As the current i in this coil changes, an induced emf will be set up in the second coil to give a value for the B-field. Consider a ring that is evenly wound with N = 200 turns of wire and has an average circumference, L = 0.50 m and cross sectional area, A = 4.0010-4 m2. It is required that the magnetic flux through the ring to be, m = 4.0010-4 T.m2. (b) What is the required value for the B-field? (c) If the torus has an air core, what current I is required to produce the above magnetic flux m ? (d) If the torus has an iron core whose hysteresis curve is given above (for the calculation, only use the magnetization part of the curve M H), what current is needed to give the required magnetic flux m ? (e) What are the permeability µ and the relative permeability µr of the iron used in your calculation for part (d)? (f) If an air gap, a = 1 mm in length is cut in the ring, what current I is required to maintain the same magnetic flux? (g) Compare the current through the coil windings for the three cases. 4