Explain cylindrical coordinate systems.
[7 marks]Transform the given vector A=10 a into spherical coordinates at Point z P (r=4, θ=110°, Ø=120°).
[3 marks]Explain cross product and dot product in detail.
[4 marks]Find Eat P (1, 5, 2) in free space if a point charge of 6 μC is located at Q(0, 0, 1), a uniform line charge of 180 nC/m lies along the z axis and a uniform sheet charge 25 nC/m2 lies in the plane z = -1
[7 marks]Define volume surface and line charge density.
[3 marks]Explain coulombs law and field intensity.
[4 marks]Given the field D = 6ρsin (φ /2) a + 1.5ρcos (φ /2) a C/m2. ρ φ Evaluate both sides of the divergence theorem for the region bounded by ρ= 2, 0 < φ < 180°, 0 < z < 5.
[7 marks]If V = 2 volts at x = 1mm and V = 0 volts at x = 0. Find Ex at x = 1 mm in free space for the volume charge density -3×108 ε x C/m3.0
[4 marks]What do you mean by equipotential surface?
[3 marks]State and prove maxwell’s first law in integral form.
[4 marks]Derive the equation to find energy stored in the field of a system of charges.
[7 marks]Find the gradient of the following scalar field = e-z sin 2x cosh y.
[3 marks]Write short note on boundary condition for perfect dielectric.
[7 marks]Explain ampere’s circuital law
[4 marks]Derive the expression of following capacitor: 1) coaxial 2) Spherical
[3 marks]Derive Poission’s and Laplace’s equation.
[4 marks]Write short note on magnetic boundary conditions
[7 marks]Explain biot-savart law.
[3 marks]Verify Stoke’s theorem for the field H = 6xya – 3y2 a and the x y rectangular path around the region 2 ≤ x ≤5, -1 ≤ y ≤1 and z = 0. Let the positive direction of ds be a . z
[7 marks]Explain skin effect.
[4 marks]Derive an equation of force on moving charge under effect of EM field.
[3 marks]Explain wave motion in free space.
[4 marks]Explain point and integral form of Maxwell’s equations.
[7 marks]Define with respect to plane EM waves: 1) Phase 2) Phase constant 3) Phase velocity
[3 marks]State and prove pointing vector theorem.
[7 marks]