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Module -2 For theory descriptive type questions please refer “A textbook of Integrated Engineering Physics” by Dr. Amal Kr. Chakrabarty 1 (i) State and explain Coulomb’s law in electrostatics. Express it mathematically with meaning of each symbol for two point charges. Does it depend on the medium property? If yes, then answer, how? What is the most important requirement for the validity of Coulomb’s law? Show that gravitational force can be neglected when compared with Coulomb’s force. (i) (ii) (iii) (iv) (v) Refer Page 48 Refer Page 48 Refer Page 49 Refer Page 49 Refer Page 50 (i) Define electric field E and electric potential V at a point and how they are related. (i) (ii) (iii) Refer Page 49, 55, 66 Refer Page 65 Refer Page 66 (ii) (iii) Show that E 0 . In a place the electric potential is same everywhere. What is your understanding about the electric field intensity in that place? State and explain Gauss’ law in electrostatics. What are its limitations? Derive Coulomb’s law from Gauss’ law. Write down the differential and integral form of Gauss’s law. Using Gauss’ law, find the electric field intensity outside, inside and on the surface of (a) uniformly (i) (ii) (iii) Refer Page 61, 64 Refer Page 76 Refer Page 63 (ii) (iii) (iv) (v) 2 3 (i) (ii) (iii) 4 a. a. Refer Page (a) 75 and (b) 74 5 6 7 8 charged sphere (b) hollow charged cylinder. Also show the graphical representation. b. The amount of net charge enclose by a closed surface is known, but there is no idea about the distribution of charges. In this case, can Gauss’ law be applied to determine the electric field intensity at any point of closed surface? Explain. a. Extend Gauss’ law to Poisson’s equation. When does it reduce to Laplace’s equation? b. Write down Laplace’s equation in Cartesian coordinate system. Two infinite parallel plates at z=0 and z=a are maintained at potentials V0 and Va respectively. Obtain the variation of potential and field between the plates. Write down Laplace’s equation in Spherical co-ordinate system and find the solution for spherical capacitor considering the variation of potential along radial direction. Write down Laplace’s equation in cylindrical co-ordinate system and find the solution for cylindrical capacitor considering the variation of potential along radial direction. (i) Define electronic polarizability and Show ε (ε −1) (ii) (iii) that α = 0 r . N Show that D =ε0E + P. What happens when a non-polar molecule is placed in an electric field? b. Within any point of the closed surface, it is not possible to find the electric field but it is possible to determine the field outside the surface. a. Refer Page 77 b. Refer Page 80 Refer Page 81 Refer Page 82 (i) (ii) (iii) Refer Page 105 and 106 Refer Page 101 Refer Page 94 9 10 a. An amount of charge Q is divided into two particles. Find the charge on each particle so that the effective force between them will be maximum. b. Check whether the field E= 4yi – 2xj + k is conservative. c. If E= q/(4πε0r2) r then show that E is solenoidal. a. If the potential in the region of space near the point (-2m, 4m, 6m) is V= 80x2 + 60y2 volt, what are the three component of electric field at that point? b. If the electric field on a region a. q, Q-q and F Kq(Q q) F 0 2 r q b. check if E 0 c. .E 0 a. E V ( 2,4,6) b. E.(75kˆ) c. 1 1 2 3 is E 4iˆ 6 ˆj 7kˆ find the electric flux through the surface area of 75 square units in XY plane. c. S1 and S2 are two hollow concentric spheres enclosing charges Q and 2Q respectively. What is the ratio of electric flux through inner surface S1 and outer surface S2? 11 a. For positive x, y and z, let V = 40 xyz c/m3. Calculate the total charge for the regions defined by (i) 0 x, y, z 2 . b. The electric potential V(x) in a region along the x-axis varies with distance x (in meter) according to the relation V(x) = 4x2. Calculate the force experienced by 1 mC charge placed at point x= 1m. 2 a. 2 2 dxdydz v x 0 y 0 z 0 b. E V ; F qE 12 In cylindrical coordinates ( , , z ) , .D electric flux density is given by ˆ zˆ . z cos 2 zˆ ˆ z D z cos 2 zˆ C/m2. Calculate the ,3 and the 4 charge density at 1, total charge enclosed by the cylinder of radius 1 meter with 2 z 2 meter. 13 a. A dielectric material contains 2 × 109 polar molecules/m3 each of dipole moment 1.8 × 10–27 cm. Assuming that all of the dipoles are aligned towards electric field E = 105 V/m. Find the polarization, electric susceptibility and the relative permittivity. b. The dielectric constant of helium at 0°C is 1.0000684. If the gas contains 2.7x1025 atoms/m3, find the radius of the electron cloud. ,3 4 At 1, And Q dV 1 2 2 2 d d dz 0 0 z 2 P ;r K 1 0 E a. P n p; b. K 1 4 na 3