Q-Bank_All Chapter_TOE-160906_6th Electrical

Ch: 1 Vector Analysis
1)	Define: 1) Vector, 2) Scalar, 3) Unit Vector, 4) Position Vector, 5) Scalar projection, 6) Vector Projection.
2)	Explain dot product and cross product of two vectors.
3)	Explain unit vectors of Cartesian, Cylindrical and Spherical co-ordinate systems.
4)	Find expression for different length, area and volume for cylindrical system.
5)	Given the point A(x=5,y=4,z=3) and B (r=6, θ=450 Φ=100) find : 1)The spherical coordinate A , 2) The Cartesian coordinate of B, 3) The Distance from A to B.
6)	Example of different co-ordinate conversation system. Given points A( x = 5, y = 1, z = -4) and B(ρ= 3, Φ = -30, z = 5), find a unit vector in cylindrical  ordinates at point B directed towards point A.
7)	Obtain the spherical co-ordinates of 2 āx+3 āy+4 āz at the point P(x= 4, y =1, z = 3)
Ch : 2 Electrostatic Field in free Space
Ø Coulomb’s law and Electric field intensity
8)	Describe coulomb’s law and Electric field intensity.
9)	Define electric field intensity. Obtain the expression for the electric field intensity at a point which is at a distance of R from a point charge Q.
10)	Derive expression of electric field intensity due to a uniform line charge over z-axis Having  a charge density of C/m.
11)	The finite sheet 0 ≤ x≤ 1, 0≤y≤1 on the z = 0 plane has a charge density ρs = xy (x2 + y2 + 25)^3/2 nC/m2. Find: 1) The total charge on the sheet, 2) The electric field at (0, 0, 5),
12)	Derive the expression for total electric field intensity due to infinite surface charge distribution in free space.
13)	Find Ē at the origin if the following charge distributions are present in free space : a) point charge 12 nC at P (2,0,6), b) uniform line charge density 3nC/m at x = - 2, y = 3, c) uniform surface charge density 0.2 nC/m2 at x = 2.
Ø Electric flux density, the Gauss’s law and Divergence
14)	State and prove the Gauss’s law. Also state the conditions to be satisfied by the special Gaussian surfaces.
15)	Application of gauss’s law-To find electric flux density due to a uniform line charge.
16)	Define divergence and its physical significance with example.
17)	D=2y2z2 āx +3xy2z2 āy +2xyz āz pc/m2in free space. Find (a) Total flux passing through the surface x=2,  0 ≤  y ≤  4, 0 ≤ z ≤ 3in a direction away from the origin , (b) The total charge contained in incremental sphere of a radius 1µm cantered at p (5,5,5)
18)	Explain Gauss’s law applied to differential volume element with usual expression.
Ø Energy and Potential
19)	Explain potential and potential gradient. Derive relationship between potential and electric field intensity.
20)	Explain electrical dipole. Also derive expression of E due to an electric dipole.
21)	An electrical dipole located at the origin in free space has a moment P = 2 āx+3 āy+4 āz nC. Find (A) find V at PA (1,2,3).
22)	Write short note: Electrostatic boundary conditions between perfect dielectrics.
23)	Given the potential field,V= 2x2+3zy2, and a point P(2, 5, 1), find following at point P: (1) the potential V, (2) the electric field electric flux density D, and (5) the volume charge density .
Ch : 3 Electrical Field in material Space and Boundary Condition
Ø Current,  Conductor
24)	Derive the relation between I and J and explain the continuity equation of steady electric current in integral form and point form.
Ø Dielectrics and Capacitance
25)	Write short note: Electrostatic boundary conditions between perfect dielectrics.
Ø Poisson’s and Laplace’s equation.
26)	Derive Poisson’s and Laplace’s equation.
Ch 4 : Steady Magnetic Field
27)	State and explain Biot-Savart’s law.
28)	Write short note on Stoke’s theorem.
Ch : 5 Magnetic Forces and Materials and Inductance
29)	State and Explain Lorentz force equation on charge particle. Also explain concept of magnetic torque.
30)	Write short-note on ‘ magnetic materials’
31)	State and Explain Ampere circuital law.
Ch : 6 Time Varying Fields and Maxwell’s Equations
32)	State Maxwell’s equations in point form and explain physical significance of the equations.
33)	Write and explain differential and integral forms of Maxwell’s equations.
Ch : 7 Analytical and Numerical techniques
34)	Explain briefly finite element method. Also state the advantages and disadvantages of finite element method.
35)	Write a short note on advantages and applications of numerical techniques in engineering.