BPHCT-133 EM 2025 SOLVED ASSIGNMENT

Description

Tutor Marked Assignment
ELECTRICITY AND MAGNETISM
Course Code: BPHCT-133
Assignment Code: BPHCT-133/TMA/2025
Max. Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.
PART A
1. a) If u  is a constant vector show that u r u    
2 ) (     . (5)

b) Determine the work done by a force j i F ˆ ) ( ˆ ) 2 ( y x y x    

in taking a particle along
the curve t t y t t x sin 4 ) ( ; cos 2 ) (   from 0  t to 4
  t . (10)
c) Using Stokes’ theorem, prove that curl of a conservative force field is zero everywhere.
(5)
d) Determine the directional derivative of the scalar field ) ln( 2 2 2 z y x     in the
direction ) k j i ( ˆ ˆ 2 ˆ   at the point (1,-1, 2). (5)
2. a) Explain with the help of diagrams what spherically and cylindrically symmetric
charge distributions are. What is the electric field at a point inside a hollow
metallic sphere of radius R having volume charge density ? (8+2)
b) Determine the electrostatic force and electrostatic field on a charged particle located at
A in the Figure given below due to the charged particles situated at B and C. The value
of the charge on each of these particles is indicated in the Figure.

Express your result both in the unit vector notation and as magnitude. (10)
c) Two particles carrying 4C and  2C charges are placed on a 1 m long straight wire.
Determine the point on the line joining these particles where the electric potential is
zero with reference to the positively charged particle. (5)

40 cm
( 5  C)
A
z
B
x
C
( 5  C) (+ 1  C)
y
50 cm
4

PART B
3. a) Explain the phenomenon of polarisation of a dielectric. Show that, when a
dielectric material is filled between the plates of a capacitor, the value of
capacitance increases by factor of K, the dielectric constant of the material. (5+10)
b) The energy of a capacitor is 4.0 J after it has been charged by a 1.5 V battery.
Calculate its energy when it is charged by a 6.0 V battery. (5)
c) A horizontal, straight wire carrying 12.0 A current from west to east is in the
earth’s magnetic field B. At this place, B is parallel to the surface of the earth,
points to the north and its magnitude is 0.04 mT. Determine the magnetic force on
1 m length of the wire. If mass of this length of wire is 50 g, calculate the value of
current in the wire so that its weight is balanced by the magnetic force. (5+5)
4. a) A current is flowing in an infinitely long straight wire. Using Biot-Savart law, show
that the resultant magnetic field at a point along a line perpendicular to the wire is
inversely proportional to the distance of the point from the wire. (5)
b) Using Maxwell’s equations in free space, derive the wave equation for the electric
and magnetic field vectors. (5+5)
c) The expression of the electric field associated with an electromagnetic wave in
vacuum is given by
) + 10 2 ( sin ˆ ) Vm 800 ( 8 1 kz t     x E


Determine the wave number, frequency, the direction of propagation and the
magnitude and direction of the magnetic field associated with the wave. (15)
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