IGNOU BPHCT-133 June 2025 Previous Year Question Paper

Q1.Answer any five parts : 8255-15

(a) Determine the gradient of the following scalar field : f =2ysinz—xy at the point (है).

(b) Calculate the line integral of the vector field : along a curve F(t) =ti+tj+th with 1<t<2.

(c) Two point charges +3q and +q at rest are placed at a distance ‘a’ from each other. Determine the position of a charge +q placed on straight line joining these two charges, if it is in equilibrium.

(d) A Gaussian surface of cylindrical shape (of radius 1.0 m and height 10 m) encloses a few positive charges. Assuming that the electric field due to these charges is normal to the Gaussian surface and has magnitude 1000 NC", calculate the volume charge density of the charge distribution.

(e) A thin dielectric rod of cross-section A extends along x-axis from x =0 to x =L. The polarization of the rod is along its length and is given by : Obtain the bound volume charge densities and the surface charge densities at each end of the rod.

(f) A long straight conducting wire carries a current of 20 A. Determine the magnitude of the magnetic field at a perpendicular distance of 0.30 m from the wire.

(g) A typical ignition coil (made of two coils) draws a current of 2.0 A, and supplies an e.m.f. of 25 kV to the spark plugs. If the current in the two coils is interrupted every 0.08 ms, what is the mutual inductance ?

(h) The electric field of an electromagnetic wave in vacuum is_ given’ by E E Qn 7 ५८ 50, ./ 5 30008 3 x—-2nx10't|, E, =0, where E is in Vm", t ins and x is in m. Determine the frequency v and wavelength i.

Q2.Answer any five parts : 5x5=25

(a) Evaluate the integral using Stokes’ theorem : pA-di 7 > 22 27 where A=(8x-y)i -—2yz"j-2y°zk and C bounds the surface S of the sphere x ty? $27 =16, z>0.

(b) Using Gauss’ divergence theorem, evaluate the following surface integral : fh, u-ndS where v’=xsin” yi + 10 xzj +zcos" yh and S is the surface of a sphere with its centre at origin and radius 2 units.

(c) Consider a parallel plate capacitor made up of two rectangular plates of area of cross-section 7.5x10m? and separated by a distance of 2x10°m. A voltage of 90 V is applied across the plates. If a dielectric material of dielectric constant 6.5 is introduced between the plates of the capacitor, calculate :

(i) Capacitance of the capacitor Gi) Electric displacement D.

(d) Determine the electric field due to an electric dipole at the midpoint of its axis.

(e) Calculate the work done to transport an electron from + ve terminal of a 9 V battery to its — ve terminal.

(f) A toroid of mean circumference 0.50 m has 300 turns, each carrying a current of 0.01 A. Calculate the value of H and B of the toroid has an air core. Calculate the value of B and the magnetisation M if the core is filled with iron of relative permeability 4000.

(g) A solenoid is 0.8 m in diameter and

Q3.0 m long. The magnetic field at its centre is 0.30 T. Estimate the energy stored in the magnetic field of the solenoid.

(h) The speed of light in a dielectric medium is one-third its value in vacuum. Calculate the refractive index and dielectric constant of the medium.

Q4.Answer any one part : 1x10=10

(a) State Gauss’ law. Two concentric thin spherical shell of radii Ri and Re (with R,>R,) carry uniformly distributed charges Qi and Qe respectively. Use Gauss’ law to determine the electric fields at the distance r from the centre for 060) r<R,, Gi) Ryg<r<R, and

(iii) r>Ry. 10

(b)

(i) State Biot-Savart’ss law. Deduce an expression for magnetic field B due to a long straight wire carrying current I. If 1=10A, determine the magnitude of the magnetic field at a perpendicular distance of 0.1 m from the straight wire. 5

(ii) Obtain the condition for the electromagnetic field described by : 2 E E = E,2 (cos kx cos ky cos wt) 2 A . and B= Bo(xcoskxsinky— ysin kx cos ky) sin wt to satisfy the following : Vx B = Lek : 5 ce at (G@) aH PO) =ti+ij+th & afem i<t<2 F E E Qn 7 E, =0 wel E, Vm! 3%, ¢ Aes Fa x He fA-dl we = A=(8x-y)i —2y27] - 2Qy7zh तथा x+y? +27 =16, z>0 Wet v’=xsin? yi +10 xz) +zcos” yk और 8

(ii) # 2 1५ । 10 E = Ep2Z (cos kx cos ky cos wt) 2 A . B=Bo(xcoskx sin ky — ysin kx cos ky) sin wt vx B = L ee c? at