IGNOU BPHCT-133 June 2023 Previous Year Question Paper

Q1.Answer any five parts : 3 each

(a) The height of a hill is given by 2100 2 .z xy Calculate the maximum rate of change in the height of the hill at the point (1, 2). What is its direction ?

(b) A two -dimensional force field i s defined as :  ˆˆF k yi xj where k is a constant. Calculate the work done by this force in taking a particle from along the path 2yx from

(c) Two identical charged particles are placed at rest at a separation of 2.0 m. What is the charge on them if the magnitude of electrostatic force exerted on each particle is 1.0 N ?

(d) The linear charge density of the inner copper wire in a coaxial cable is +  and that of the outer copper wire  . What is the electric field at

(i) a point lying i nside the inner wire and

(ii) a point outside the coaxial cable ? Explain.

(e) Calculate the effective capacitance of three capacitors arranged in such a way that two of them ( 1C and 2C ) are in series and the third ( 3C ) is in parallel with this series combination.

(f) A long straight wire carries a uniformly distributed current. At what distance from the axis of the wire will the mag nitude of the magnetic field be maximum ? Justify your answer.

(g) The magnetic flux through the coil perpendicular to its plane is given by milliweber. Calculate the magnitude of the e .m.f. induced in the coil at t = 3 s.

(h) The magnitude of the maximum electric field associated with an electromagnetic wave travelling in vacu um is 1500 Vm –1. Determine the mangitude of the maximum magnetic field associated with the wave.

Q2.What is the wave’s direction of propagation if the electr ic field is in the positive z-direction and the magnetic field in the positive x-direction ?

Q3.Answer any five parts : 5×5=25

(a) Using Stokes ’ theorem, evaluate  C A. dl where     22ˆ ˆ ˆA2 x y i yz j y z k and C is the boundary of the ellipse 1;49 0z  in the xy-plane.

(b) Use the divergence theorem to evaluate : A . Sd where ˆ ˆ ˆA xi yj zk    and S is the surface of the sphere

(c) Two parallel conducting plates of area of cross-section 2.0 m 2 are separated by a distance of 1.0 × 10–2 m. The potential difference  0V between vacuum is 2000 V. When a dielectric sheet of thickness 1.0 cm is introduced between them, t he voltage is found to decrease to 1000 V. Calculate

(i) the dielectric constant

(ii) the permittivity

(iii) the susceptibility,

(iv) electric field between the plates in vacuum

(v) elective field in the dielectric.

(d) Three particles each having charg e 1.0 are placed at the vertices of an equilateral triangle with each side of length 1 m. Calculate the magnitude of the net electric field at the midpoint of any side of the triangle.

(e) The potential of a certain charge configuration is expressed as 223x xy y (in V). Determine the acceleration of an electron at the point (5, 2) in the x-direction. Distances are measured in metres.

(f) A toroid of aluminium having length 50 cm is closely wound by 50 t urns of wire carrying a steady current of 1.0 A. The magnetic field in the toroid is found to be

Q4.5 × 10–4 Wbm–2. Calculate the relative permeability.

(g) State Lenz’s law. When a sheet of copper is pulled out in a mag netic field perpendicular to it, a resisting force is exerted on it. Explain why.

(h) A plane electromagnetic sinusoidal wave in vacuum is characterized by the following parameters :

(i) Wave is travelling in the – ˆx direction.

(ii) Its frequency is 50 MHz.

(iii) The associated electric field is perpendicular to the direction ˆz .

(iv) The amplitude of the electric field is 50 Vm–1.

Q5.Write down the expression s for  and fields that specify this wave.

Q6.Answer any one part :

(a) State Gauss’ law. A solid cond ucting sphere of radius 1r carries charge + Q and is concentric with a thin conducting spherical shall carrying a charge + 2Q and radius  21rr  . Determine the electric fields of a distance r from the centre of the sphere for

(i)

Q7.rr

(ii) 12r r r , and

(iii) 2rr . 10

(b)

(i) State Ampere’s law. Using it deduce an expression of the magnetic field due to a solenoid of n turns per unit length of wire carrying a current I0. 5

(ii) Write Maxwell’s equations in vacuum. Derive the wave equation for the field. 5 Value of physical constants : 9 2 2 1 9 10 Nm C4