Engineering Electromagnetics — Winter 2018

Explain the concept of dot product and vector product with the help of proper equations and vector diagrams.

State Coulomb’s law. Derive the expression for following: i. Scalar & Vector form of Coulomb’s law, ii. Electric field intensity.

What do you mean by boundary conditions? Derive the boundary conditions at the interface between two dielectric materials with permittivities ε and ε .12

Write down point and integral forms of all four Maxwell’s equations for steady & time-varying electro-magnetic fields.

An infinitely long coaxial cable is carrying current Iby the inner conductor of radius ‘a’ and –Iby the outer conductor of radii ‘b’ and ‘c’, where c>b. Derive the expressions for Hat (i) ρ < a, (ii) a < ρ < b, (iii) b < ρ < c, (iv) ρ > c.

Using del operator, explain the following in brief: i. Gradient of a scalar ii. Curl of a vector

Write a detailed note on the divergence & its physical interpretation.

Derive the expression for the following: i. The divergence theorem ii. Stoke’s theorem

Illustrate the concept of skin depth and skin effect in good conductors.

Derive i. Maxwell’s 1st equation for electrostatics ii. Maxwell’s 3rd equation for electrostatics.

Given the potential field V=2x2y - 5z, and a point P(-4, 3, 6), find following at point P : the potential V, the electric field intensity E, the direction of E, the electric flux density D, and the volume charge density ρ . v

Derive i. Lorentz force equation ii. Point form of Ohm’s law.

Three infinite uniform sheets of charges are located in the free space as follows: 3 nC/m2 at z = - 4, 6 nC/m2 at z = 1, and -8 nC/m2 at z = 4. Determine Eat the point P(2, 5, -5) & Q(4, 2, -3).

Acurrent filament carrying 15 Ain the a direction lies along the entire z axis. z Find Hin rectangular coordinates at: (i) P (201/2, 0, 4). A1

Find the magnitude of current density in a sample of silver for which σ = 6.17 × 107 S/m and µ = 0.0056 m2/V·s if: (a) the drift velocity is 1.5 µm/s; (b) the e electric field intensity is 1 mV/m; (c) the sample is a cube 2.5 mm on a side having a voltage of 0.4 mV between opposite faces; (d) the sample is a cube 2.5 mm on a side carrying a total current of 0.5 A.

Determine an expression for the volume charge density associated with each of the following Dfields:

D = 4xy/z a + 2x2/z a – 2x2y/z2 a ; x y z

D = z sinφ a + z cosφ a + ρ sinφ a ; ρ φ z

Aslab of dielectric material has a relative dielectric constant of 3.8 and contains a uniform electric flux density of 8 nC/m2. If the material is lossless, find: (a) E;