Engineering Electromagnetics — Winter 2019

Explain Cylindrical co-ordinate system with a neat sketch giving details of their unit vectors and point form and vector form representations.

Define curl and give its physical interpretation. Also give relation of curl in all three co-ordinate system.

State Coulomb’s law and give its mathematical expression. From that deduce expression of electric field intensity Efor point charges.

Find Electric Field Intensity Eat a point on Z-axis, due to circular ring charge with charge density ρL C/m present in XY plane.

State and prove divergence theorem. Relate Gauss’s law with divergence theorem.

State & explain the Biot-Savart’s Law and derive the necessary equations of Magnetic field Intensity H.

Acircular loop located on X2 + Y2 =9, Z=0 carries a current of 10 Aalong â . ǿ Determine Hat (0,0,4) and (0,0,-4).

Acircular current carrying loop is lying on x-y plane. Derive the equation of Magnetic field intensity Hon the axis of a circular loop. Also find Hat the center of the loop.

Evaluate Stoke’s theorem for the field H = 6xy â - 3y2 â amp/meter if rectangular x y path around the region is 2 ≤ x ≤ 5, -1 ≤ y ≤ 1 and z=0. Also find out current I.

Derive electrostatic Boundary conditions for Dielectric to Dielectric interface.

Find the potential and volume charge density at P (0.5, 1.5, 1) in free space if potential field is given as V = 6 ρɸz.

Aboundary exist at z=0 between two dielectric. ε = 2.5 in region z<0. ε = 4 in r1 r2 region z>0. The electric field in the region of ε is E = -30 â + 50 â + 70 â V/m. r1 1 x y z then find out i. Normal component of E1 ii. Tangential component of E1 iii. Angle ϴ between Eand normal to the surface11 iv. Normal component of D2 v. Tangential component of D2 vi. Angle ϴ between Eand normal to the surface22

Define Torque. Derive the equation of Torque on a close current carrying loop which is placed in steady magnetic field.

Derive Maxwell’s equations in point and Integral form for time varying fields.

Derive the equation of Capacitance (C) and Energy stored (W) for parallel plate capacitor.

Explain wave propagation in free space with necessary equations.

Derive point form of Ampere’s Circuital Law.