Mumbai University Previous year question papers

Electromagnetic Wave Theory

N.B.(1) Question No.1 is compulsory. .

(2) Attempt any four questions out of remaining six questions.

(3) Assume any suitable data if necessary.

(4) Figures to the right indicate full marks.

1. Attempt any four of the following :-

(a) Prove that the curl of the gradient of a scalar function i~ zero.

(b) State the defining conditions of special gaussian surface.

(c) State and explain Amperes. circuita.1law.

(d) Prove that a static electric field is irrotational and the static magnetic field is solenoidal.

.(e) Showthat the electrostatic energy stored in g parallel plate capacitor is given by ~ cv2

2. (a) Derive an expression for the Electric field Intensity due to an infinite sheet charge.

(b) Charge lies in the z =3m plane in the form of a square sheet defined by 2 5 x 5 2m, – 2 5 Y 5 2 m. with charge density Ps = 2( X2 + y2 + 9)3/2 nc/m2. Find E at the origin.

3. (a) Given that

0=( 1~:3)ax c/m2, evaluate both sides of the divergence theorem for the volume of cube, 2 m on an edge, centered at the origin and with edges parallel to the axes. .

(b) For a line charge PL =( 10;9 }c/m on the Z – .axis find VASwhere A is (2m, ~, 0) and B is (4m,n, 5m).

4. (a) Find the capacitance of a co-axial conductor of length /, where inner and outer radii are Y1of Y2respectively 60sinO

(b) If V = r2 volts in free space and. point P is located at r = 3m, 8 = 60 and  25°, find

(i) V at p

(ii) E at P (iii) ~~ at P (iv) c\, at P (v) Pv at P.

5. (a) Using Biot Savart law find the magnetic field intensity at any pt. P due to a finite length conductor placed along Z-axis.

(b) Evaluate both the sides of Stoke’s theorem for the portion of the sphere specified byr=4m,05850.1 n, 05 ~50.3n. Given H =6rsinljlar+18rsineCOSljlaljl’

6. (a) State and explain Maxwell equation for time-varying fields.

(b) If v = vm sin wt is the voltage applied to a capacitor and I is the current flowing through it, then show that the displacement current through the capacitor is equal to the conduction current I.

7. (a) Define Poynting vector. Obtain the integral form of the poynting theorem and explain each of the terms.

(b) A lossy dielectric has ~r = 1,E r ~ 50 and 0″.:::; 20 mho/sat 15.9MHz,electromagnetic wave propagating through this medium. Find attenuation constant a, phas