EC3452 Electromagnetic Fields Important Questions

EC3452 Electromagnetic Fields

Important Questions

Unit 1

1. Analyze the Gradient of scalar and divergence and curl of the vector.
2.  Find the gradient of the scalar fields U = x ^ 2 * y + xyz and U = e ^ (- x) * sin 2x * cos y .
3. Convert points P(1, 3, 5) and T(0, – 4, 3) from Cartesian to cylindrical and Spherical coordinates.
4. 
   

   

5. Given, A=(sin2p) ao in cylindrical co-ordinates. Find curl of A at (2, π/4,0).
6. Given the two points, A(x = 2, y = 3, z=1) and B=(r=2,0 = 20°, φ = 220°). Find
   (i) Spherical co-ordinates of A
   (ii) Cartesian co-ordinate of B.

Unit 2

1. A charge is distributed on x axis of Cartesian system having a line charge density of 3 X² µC/m. Find the total charge over the length of 10 m.
2. If D= (2y ^ 2 + z) vec a x +4xy vec a y +x vec a z C/m^ 2 find
   (1) The volume charge density is at (-1, 0, 3).
   (2) The flux through the cube is defined 0 <= x <= 1 0 <= y <= 1 0 <= z <= 1 by
   (3) The cube encloses the total charge.
3.  Rearrange Gauss’s law and develop Laplace’s and Poisson’s equations.
4.  Interpret the Electric Flux density for a uniformly charged sphere of radius ‘a’. Construct a Gaussian surface for the case of r >= a and r <= a separately.
5. A parallel-plate capacitor has a plate area of 200m ^ 2 and a plate separation of 3 cm. The charge density is with air dielectric. Determine (1) The capacitance of the capacitor.
   (2) The voltage between the plates
6. If V=x-y+xy+2z V, Find
   (i) E at (2, 2, 1)
   (ii) Energy stored in a cube of side 1m centered at the origin.

Unit 3

1. Prove that total magnetic field intensity (H) outside of the outer coaxial conductor is zero for infinitely long coaxial transmission line using Amperes law. Determine H at each Amperian path.
2.  Determine the Magnetic field and current distributions for the following three conditions
   (i) Infinite line current along the z-axis
   (ii) Infinite sheet of current
   (iii) Infinitely long coaxial transmission line
3. Obtain the expression for magnetic field intensity on an axis of a circular ring.
4. Find the magnetic field intensity at a point P, due to a finite straight conductor, carrying a current I.

Unit 4

1. A thin ring of radius 5 cm is placed on plane z1 cm so that its center is at (0, 0, 1) cm. If the ring carries 50 mA a,, find H at (0, 0, 1) cm and (0, 0, 10)cm.
2. Prove that Maxwell’s equations are related to time-varying magnetic fields.
3.  Reconstruct Ampere’s circuit law for time-varying situations to satisfy Faraday’s law.
4. Derive the Helmholtz’s wave equations for both E and H fields.
5. Derive wave equation, and explain the properties of uniform plane waves in free space.
6. Derive and explain, Maxwell’s equations both in integral and point forms.

Unit 5

1. Conclude that the tangential components of H are discontinuous across the boundary, and the normal components of H are continuous across the dielectric-dielectric boundary medium. Besides, determine H’s tangential and normal components across the dielectric-conductor boundary medium.
2. A uniform plane wave propagating in a lossless medium has E=2sin[10⁸t-ßz]ä, V/m. If 6,1, μ, = 2 and σ=-3V/m, characterize the medium. Compute the nẞ and H.
3. If the wave encounters a perfectly conducting plate normal to the z-axis at z=0, find the reflected wave E, and H,.
4. Derive pointing vector in integral and point form from Maxwell’s equation.
5. Explain the reflection of plane wave by conducting medium, under normal incidence.