Engineering Electromagnetics — Winter 2020

i) Express point P(-2,6,3) in the cylindrical and spherical co-ordinate system. ii) Explain Dot product and Cross product in brief.

Define Coulomb’s law and derive the expression for electric field intensity E due to point charge.

State Gauss’s law and derive the Maxwell’s first equation. Determine Electric flux density Dfor spherical Gaussian surface with point charge at the center.

Two dipoles with dipole moments -5a nC/m and 9a nC/m are located at points z z (0, 0,-2) and (0, 0, 3) respectively. Find the potential at the origin.

Explain Uniqueness theorem in detail.

Derive an expression for the capacitance of spherical capacitor.

State and derive Biot-Savart’s Law.

Explain Maxwell’s equations in Point and Integral Form.

Explain how plane wave moves in free space with help of the neat diagram.

Derive magnetic boundary conditions for Band Hbetween two magnetic mediums.

Derive the expression of the Poynting vector.

Generate the expression for Continuity of current.

Derive magnetic dipole moment for the rectangular planar loop in a uniform magnetic field.

Acylindrical capacitor has radii a= 1cm. and b=2.5 cm. If the space between the plates is filled with an inhomogeneous dielectric with ɛ (10 + ρ)/ ρ, where r = ρ is in centimeters, find the capacitance per meter of the capacitor.

Explain Faraday’s law with neat diagram.

For a vector field Ashow that, the divergence of the curl of Ais zero.