Engineering Electromagnetics — Summer 2019

Define Coulomb’s law. Derive the expression for the intensity of electric field due to a line charge along the Zdirection with uniform charge density ρ c/m. L

State and prove Uniqueness theorem.

Derive the expression of gradient of scalar field in all the systems and list computational formulas on gradient.

Given point P(-2,6,3) and vector A= ya + (x + z)a , express Pin cylindrical x y and Spherical coordinates. Evaluate Aat Pin the Cartesian and Cylindrical systems.

Determine the divergence of these vector fields.

P = x2yz a + x z a x z ii) Q = ρ sinØ a ρ + ρ2 z a Ø + z cosØ a z iii) T = 1/r2 cosθ a r + r sinθ cosØ aθ + cosθ a Ø

Define electric dipole. Derive expression for electric field intensity at point ‘P’ at distance ‘r’ from center of dipole at origin along Zaxis

Describe the electric boundary condition between free space and conductor. Explain the importance of boundary condition.

Write Maxwell’s equation in point and integral form, also explain its significance.

Derive Poisson’s and Laplace’s equations and states their applications.

State Ampere’s circuit law and derive the expression for curl of magnetic field intensity.

State and derive Biot- Savart’s law

Using Ampere’s circuit law, derive an expression for Hdue to infinite sheet of current.

Explain Faraday’s law in detail with neat diagram.

Define lossy dielectric medium. Derive expression for attenuation constant and phase constant for the same.

Aparallel plate capacitor with plate area of 5 cm2 and plate separation of 3mm has a voltage of 50 sin103t Vapplied to its plates. Calculate the displacement current assuming ɛ = 2ɛ 0.

State and derive Poynting’s theorem.

In a nonmagnetic medium E= 4 sin(2 X 107t – 0.8x) a V/m Π z Find 1) ɛ ɳ r , 2) The time average power carried by the wave. 3) The total power crossing 100 cm2 of plane 2x + y =51