BPHCT-133 EM 2026 SOLVED ASSIGNMENT

Description

Tutor Marked Assignment

ELECTRICITY AND MAGNETISM

Course Code: BPHCT-133

Assignment Code: BPHCT-133/TMA/2026

Max. Marks: 100 Note: Attempt all questions. The marks for each question are indicated against it.

PART A

1.a) The height of a hill is given by . 100 2 2y x z – = Calculate the maximum rate of change (also called the steepest ascent) in the height of the hill at the point (2,1). What is its direction?

b) Consider a rigid body rotating about a fixed axis with a constant angular velocity w r , directed along the axis of rotation. The velocity v r of a particle on the rigid body is .r r r ´w Calculate .v r r ´Ñ

c) Calculate the net work done by a force j i F ˆ) ( ˆ) 2 6( 2x y x + – = r in taking a particle along the straight line between the points (5, -3) to (0,0) and then along the straight line between the points (0,0) to (5,3) . Is the force conservative? Explain.

d) Calculate the flux of a vector field k j i F ˆ 3 ˆ ˆ 2 z y x + + = r through the surface of a cube defined by 2 0;2 0;2 0 £ £ £ £ £ £ z y x .

2.a) Two positively charged particles having charges 10 mC and – 5 mC, respectively, are kept at a distance of 1 m from each other. Determine the force on each charge and the electric field due to each charge. Show the force and electric field vectors on appropriate diagrams. What is the resultant force at a point midway from the two charges along the straight line joining them? (

b) State Gauss’s Law. What does spherically symmetric charge distribution mean? Use Gauss’s Law to determine the electric field of a solid metallic sphere of radius R having volume charge density r at a point outside the sphere

c) Three capacitors are connected to each other as shown below: Calculate the equivalent capacitance between points A and B.

PART B

3.a) What do you understand by linear conductors? Discuss the conditions under which metals do not behave as linear conductors.

b) The number density of electrons in the aluminium metal is 9.64 ´ 1028 m- Calculate the drift velocity of electrons in a aluminium wire of cross-sectional area 2.0 mm2 in which a current of 4 A is flowingA B 2mF 4mF 6mF (

c) Using Biot-Savart’s law, obtain an expression for the magnetic field due to electric current flowing in a long straight wire at a distance R from the wire along a line perpendicular to the wire. d) Discuss the B-H curve for a ferromagnet.

4.a) Using Maxwell’s equations in free space, derive the wave equation for the x-component of the electric field vector. e

b) A uniform plane wave of 100 MHz travelling in free space strikes a large block of a material having = 9 e 0 , m = 4 m 0 and incident electric field vector is given by r E = 1000 cos( w t – β y ) ˆ z Vm-1 s = 0 normal to the surface. If the write the complete expressions for the incident, reflected and transmitted field vector