# Mumbai University Previous year question papers

## Electromagnetic Wave Theory

N.B.:

Question No.1 is compulsory.

Attempt any four out of remaining six.

Assumptions made should be clearly stated.

Assume data wherever required with justifications.

Figures to the right indicate full marks.

Illustrate answers with sketches wherever required.

Use legible handwriting. Use a bluelblack ink pen to write answers.

Bold letters indicate vector quantities.

1. (a) What is the relation between electric potential and electric field intensity? What do you understandby”conservativefield”?

(b) What is scalar and vector magnetic potential? Givetheir expression and significance along with their units:

(c) What is the discrepancy in Ampere’s Law? How was it removed by Maxwell?

(d) State Gauss’s law for electrostatic fields. Using Gauss’s law, derive expression for intensity due toan infinite line charge.

2. (a) Developan expressionfor Edue to a uniformchargedensity Pson an infinitesheet.

(b) Acurrent filament of 5 amp in y-directlon Is parallel to the y-axis at x=2, z=-2. FindHat the origin.

(c) Deriveexpression for the potential energy stored In a static electric field.

3 (a) Auniform line charge with PI =50pC Im liesalongthe x-axis.Whatfluxper unit length ‘¥ I L, crosses the portion of the z=-3m plane bounded by y =:1:2m?

(b) . Currentsinthe innerandouterconductorsoffigure(1)are uniformlydistributedover cross.,.sectlon.Radius of inner conductor is ‘a’ and the outer radii are ‘b’ and ‘e’ respectively. FindBeverywhere due to the cable:-

4. (a) Ifthe zero potentialreference is at r=10m, and a pointchargeQ=0.5nCis at the origin, findthe potentialsat r=5m,and r=15m.Atwhat radiusisthe potentialthe same in magnitudeas that at r=5mbut oppositeinsign?

(b) Verify Stoke’s theorem for portion of a sphere r =4, 0 ~ B ~ O.17r,O~ t/J ~ O.31f; Ii= 6rsin t/J~+18rsin ecost/J~.

5. (a) In cylindricalcoordinates, p=5mm and p=25mm have voltages of  zero and Vo respectively. If E=-8.28 }J KV 1m  at p=15 mm, find  outer conductorusinglaplace’s equation.Voand the <:harge density on the

(b) State and explain Faraday-Lenz’s law. Obtain point form and integral form of  Maxwell’s equation for induced motional and transformer emf.

6. (a) Derivegeneral wave equations for °E~andH-fields. Givesolution to the wave equation in perfect dielectric for a wave travelling in z~direction,which has only x-component of  E-field.

(b) Auniform plane waves propagates In a medium with t:r= 4,0″= Q,Pr= 1.TheE-field has only x-component which is sinusoidal with a frequency of  100 MHzand has maximum value of  0.1 mV/m at t=O,z=l/B. Findinstantaneous expression for E(z,t)and H{z,t).Alsofind the location where Exis positive maximum at t= 10 ns.

7.Writeshort notes on anvtwo:-

a) Boundaryconditionsin Electrostaticsand Magnetostatics

b) Method of  images

C) Maxwell’sequationsfor steady andtime varyingfields.