IGNOU BPHCT-133 December 2025 Previous Year Question Paper

Q1.Answer any five parts : 5x3=15

(a) Determine the unit vector normal to the curve : x? 4+6y? =1 at the point (1, 0).

(b) Calculate the work done by a force field F=xyi+y"j in moving an object along the curve y=x” in the xy-plane from (0,0) to(1,1).

(c) A point charge is enclosed by a spherical Gaussian surface. Would the electric flux through the surface change

(i) if the Gaussian surface is chosen to be a closed cylinder or a cube ?

(ii) if the charge is moved outside the Gaussian surface ?

(iii) if another charge is placed inside the Gaussian surface ?

(d) The electric field of an electromagnetic wave in vacuum is given by: E E Qn 8 1 =O, Ly = 80cos| | — |x-2n2x10°t |, E, =0 where E is in Vm", ¢ in s and x in m. Determine the frequency, wavelength, the direction of propagation of the wave and the direction of the associated magnetic field.

(e) Two point charges +q and -2q are placed along a straight line at a distance of 9 m from each other. Determine the distance of a point from the charge +q between the two charges where the electric potential is zero.

(f) A thin dielectric rod of cross-section A extends along the x-axis from x=0 to x=L. The polarization of the rod is along its length and is given by P = (ax? +b)i. Obtain the bound volume charge density and the surface charge density at each end of the rod.

(g) A long cylindrical wire of radius R carries a steady current i which is uniformly distributed over its cross- sectional area. Determine the magnetic field at a distance r(<R) from the axis of the wire.

(h) Obtain the maximum value of the displacement current in a parallel plate capacitor made up of plates of area A. The electric field between the plates is given by E= Ep sinot .

Q2.Answer any five parts : 5x5=25

(a) An AC generator consists of 20 turns square wire coil of side 50 cm. The coil is turned at 50 revolutions per second to produce the standard 50 Hz alternating current produced in the country. What must the magnitude of the magnetic field be for the peak output voltage of the generator to be 300 V ?

(b) Five very long straight insulated wires are closely bound together to form a small cable. Currents carried by the wires are i, =20A, i, =—6A,i, =12A, i;=-7A and i,=18A _ (negative currents are opposite in direction to the positive). Calculate the magnitude of B at a distance of 10 cm from the cable.

(c) Calculate the magnitude of the magnetic force exerted by Earth’s magnetic field B = 10-> T on an electron moving with speed 10° ms"! near the Earth’s surface.

(d) Write Maxwell's equations in differential form. Derive the wave equation for B field.

(e) Consider a system of four charges : 4q,q,-4q and -q. Draw a Gaussian surface enclosing at least two charges of the system so that the net electric flux through it is

(i) zero,

(ii)

(4) .

(f) Acharge of 2.0uC is kept at the origin and points A and B are located along the x-axis at a distance of 10 cm and 50 cm from the origin. Calculate the work done in bringing a charge of

Q3.0uC from point B to A.

(g) Using the Divergence Theorem, calculate the flux of a vector field : F=2i +4yj —x°h over a sphere of radius 1 unit.

(h) A central force field is a force field of the form F- f(r)?. Determine V x F

Q4.Answer any one part: 1x10=10

(a) Determine the electric potential V of a uniformly charged non-conducting sphere of radius R at a point P located at a distance ‘r’ from the centre of the sphere (r<R).

(b) State Biot-Savart’s law. Determine the magnetic field B at a point P located at a distance R along the axis of circular current loop carrying a current I. aa F-ayity?} oe fea wa or E, =0, E, ~ 0c {28)x-2n-a0¥r] E, =0 vel E, Vm! 3%, ¢ AHS FN x He