IGNOU BPHCT-133 December 2020 Previous Year Question Paper

Q1.Answer any five parts : 3 each

(a) Determine the gradient of the function :

(b) Determine the position vector of a particle r(t) moving with the velocity : V(t) = 2sinti -costj given that r =i+j att=0. Lot-Il 2.1. 0.

(c) Calculate the electric field of a particle carrying charge + 6.0 nC at a point 3.0 m away from it. Determine the electrostatic force exerted on an electron placed at that point.

(d) A charge of + 18 uC is placed on a hollow metal sphere of radius 0.10 m. What is the electric field at its centre ? Calculate its electric potential at a point 1.0 m from its centre. 1+2

(e) A dielectric block is polarised such that : > no ०» P = 2.0 x 10-8 (2x7i + yj + zk) Cm Determine the bound volume charge density for the block.

(0) Draw the labelled B-H curve for a ferromagnetic material and _ indicate coercivity and remanence an it.

(g) A typical ignition coil (made up of two coils) draws a current of 4.0 A and supplies an e.m.f. of 32 kV to the spark plugs. If the current is interrupted every 0.10 ms, what is the mutual inductance of the two coils ?

(h) The electric field of an electromagnetic wave in vacuum is given by : 2 . | 7 9,14 E = 50sin gv 7 nx 10 tly where E is in Vm", x is in m and t ins. Determine the frequency and wavelength of the wave and its direction of propagation. What is the direction of the associated magnetic field ?

Q2.Answer any five parts :

(a) Using Stokes’ theorem, show that a central conservative force field F is irrotational everywhere. 5

(b) Using the divergence theorem, determine the flux of the vector field : 5 > 2 no: F = 2xi + 3yj + zk through the surface of the sphere given by x2 + y2 +22 = 16. 5

(c) A charged non-conducting spherical shell having inner radius 2.0 m and outer radius

Q3.0 m carries a charge of magnitude 18 pC distributed uniformly over its volume. Determine the magnitude of the electric field due to it at a distance of 3.0 m from its centre. 5

(9) The point charges + g and — 2q are placed along a straight line at a distance of 12 m from each other. Determine the distance of a point, from the charge + q, between the two charges where the electric potential is zero. 5

(e) Two parallel conducting plates, each of area 1.0m? are separated by a distance of

Q4.0x10-%m. The potential difference between them in vacuum is 1000 V. When a dielectric sheet of thickness 2.0 cm is inserted between the plates, the potential difference between them decreases to 500 V.

(i) Calculate the dielectric constant, permittivity and susceptibility of the dielectric. 3

(ii) Determine the electric field between the plates in vacuum, and the electric field in the dielectric. 2

(f) A circular loop of radius 0.05 m consisting of 100 turns of wire carries a current of

Q5.0 A. Calculate the magnitude of the loop’s magnetic moment. Suppose that initially the magnetic moment is aligned with a uniform magnetic field of 0.50 T. What is the magnitude of the torque required to hold the loop at 90° from its original orientation ? 24+3

(g) State Lenz’s law. Using the law, explain why a metal ring placed on top of a solenoid jumps when current through the solenoid is switched on. 1+4

(h) The electric and magnetic fields associated with an electromagnetic wave are given by: 3+2 E = Ej sin (kx — wt)y and B = By sin (kx — wt )Z Determine the magnitude and direction of the Poynting vector, and the energy density of the electromagnetic field.

Q7.Answer any two parts :

(a) Derive the expression for the electric potential at a point inside a uniformly charged non-conducting sphere. 5

(b) Using Biot-Savart’s law, obtain an expression for the magnetic field at a point on the axis of a current- carrying loop. 5

(c) Write Maxwell’s equations in differential form in vacuum. Using them, derive the electromagnetic wave equation in vacuum for the electric field. 24+3 Physical constants : 1 9 20-2 —— = 9x 109 N-m?C 47780 € 5-1.6»1071१ 0

(क) OA: T(x, y) = aye