IGNOU BPHCT-133 December 2024 Previous Year Question Paper

Q1.Answer any five parts : 5x3=15

(a) Determine the unit vector normal to the curve x? +5y” =1 at the point (1, —2).

(b) Determine the work done by a force : in moving a particle along a curve in the xy-plane given by x = 2t, y=3t” from ¢ =0 tot=1.

(c) Two positive point charges Q, and Q, are

Q2.0 m apart and their combined charge is 30 uC. If one charge repels the other with a force of 0.090 N, what are the magnitudes of the two charges ?

(d) The electric field due to an infinite line charge has magnitude 7x10°NC? at a distance of 2.0 m. Calculate the linear charge density.

(e) A dielectric block is polarised such that : P=1.5x107(ai +) +4) Cm2 Calculate the bound volume charge density.

(f) A horizontal wire is carrying current from east to west. What is the direction of the force on the current carrying wire if we assume that at this location the magnetic field of the Earth points due north ? If the wire carries a current of 30 A, calculate the force per unit length on it due to the Earth’s magnetic field, which is about 10*T.

(g) A wire loop on the plane of the paper having radius 10 cm and resistance 3 Q is kept in a uniform magnetic field B at right angle to its cross-sectional area. The magnetic field points into it and increasing at the rate of 0.1 Ts’. Determine the magnitude and direction of the induced current in the loop.

(0) Obtain the maximum value of the displacement current in a parallel plate capacitor made up of plates of area 1.0 m”. It is given that the electric field between the plates is E=E) sin wt with E, =5V and frequency 15 MHz. (Take €)= 8.85x10-” Fm)

Q3.Answer any five parts : 5x5=25

(a) Evaluate fA-dl , where A=x*it+aj+z°k and C is the ellipse in the xy-plane defined by: 2 ye ¥ 47 <1 2-0. 16 64

(b) State divergence theorem. Using it calculate the divergence of the vector field > s an A =2xi +3yj+2k, over a sphere e+yte =a’,

(c) Two parallel plates, which have cross- sectional area of 90 cm”, carry equal and opposite charge of 2x10-7C. The space between the plates is filled with a dielectric material and the electric field within the dielectric is 4x10°Vm 7. What is the dielectric constant of the dielectric if the electric field across the plates without dielectric is given by E , where o is the surface charge density of the plates.

(d) Three charged particles A, B and C each having a charge of 1.00 uC, are placed at rest on a straight line. The distance between A and B is 0.01 m. What is the net electrostatic force exerted on a particle C if it is placed to the left of the particle B along the line AB at the midpoint of AB?

(e) The electric potential at any point is given by V= x(2y" - 2x), Determine the electric field E at point (1, 1).

(f) An air-core solenoid wound with 30 turns per centimetre carries a current of 0.27 A. Calculate the value of magnetic field B and magnetic intensity H at the centre of the solenoid. If an iron-core of permeability 6x10°Hm is inserted in the solenoid, what will be the value of H and B ? Take w=4nx107 Hm",

(g) A solenoid of length 1 m and diameter 15 cm has 9000 turns of wire. A current of

Q4.0 A flowing in it is reduced steadily to zero in 1.0 ms. What is the magnitude of the back e.m.f. of the solenoid while the current is being switched off ? Take py =1.26x10°Hm"™.

(h) Consider an electromagnetic wave in vaccum whose electric field is given by : n A 8 E= (30Vm™) cos (10 t+ hz). Determine the direction of propagation, the wave number, the frequency and the magnetic field of the wave.

Q5.Answer any one part: 1x10=10

(a) State Gauss’ law for electric field associated with symmetric charge distribution. Consider a spherical charge distribution of radius R having uniform volume charge density. Using Gauss’ law, obtain expression for electric field due to it at a distance r from the centre at

(i) r>R, and

(ii) r<R. 10

(b)

(i) Starting from the integral form of Ampere’s law : | B.dl= pol enclosed, obtain its differential form and hence show that B is conservative field only when current density is zero. Gi) Under what conditions, do the following time-varying electric and magnetic field : 5 2 4% E E= jE) sin(z—vt); B=iBy sin (z - vt) with E, and By as constant, satisfy the equation : vxE--23 » (@) aaa F बल F=(x-39 +(x—y)j faga aa ar cam 7x10°NC? 21 uated aif © a1,220. My = 4x10 Hm? AM aI E =(30Vm") cos (10% + kz). J Bedi=nol E=JE,sin(z—vt); B =iB, sin(z—vt)