COURSE TITLE: APPLIED ENGINEERING PHYSICS
COURSE No: BST1103 (Total= 150 marks)
SECTION-B
SECTION-A
UNIT1: ELECTROMAGNETIC FIELDS AND WAVES
UNIT-IV: SEMICONDUCTOR PHYSICS
UNIT-II: LASER PHYSICS
UNIT –V: APPLIED OPTICS
UNIT -III: QUANTUM MECHANICS
UNIT VI: FIBRE OPTICS
NOTE: There shall be a total of eight questions, four from Each Section A & Section B. Each question carries 20 marks.
Five questions will have to be attempted. Selecting at least two from each section. Use of Scientific calculator is
allowed. (100 marks)
Internal Sessional -1st
Internal Sessional -2nd
Home-Assignment-I
Home-Assignment-II
Attendance
10 marks
10 marks
10 marks
10 marks
10 marks
UNIT 1
Electromagnetic Fields and
Waves
By
Dr. Shammi Kumar
Deptt. of Physics, GCET, Jammu
Weightage= 20 marks
Topics:Concepts of Del Operator- gradient, divergence, curl and their physical significances, Displacement Current. Maxwell's
equations in integral and differential form, Poynting vector and Poynting theorem, Electromagnetic wave propagation in
free space (e m wave equations for electric & magnetic fields for free space) & their solutions (plane wave solution),
velocity of E M waves, Relation between Eo & Bo.
08 lectures
The behavior of a physical quantity in a given region of space is described by
its value at each point in that region of space.
Field:- A field is a function that describes the behavior of a physical quantity
at all points in a given region of space.
The physical quantity described by the field can be a scalar
quantity or a vector quantity.
Thus field can also be scalar filed or a vector field
Scalar Field:
• It is a function that gives us a single value of some physical quantity
for every point in space.
• In a scalar field each point will have magnitude corresponding to that
scalar quantity.
HOT
1
Cold
2
3
A
Ice
Ice
q
B
Ice
Water
drops
Fig. 1
VA
VB
Fig. 2
Representation of Scalar Field
• A scalar field is represented by imaginary surfaces known as level
surfaces.
• A level surface is a surface at which the value of a scalar is same
• E.g; equipotential surfaces, equithermal surfaces etc.
Mathematically
Φ = Φ(𝑟)
Φ= Φ(x,y,z)
Φ is a scalar quantity
Vector Field:
• A vector field is a function that gives us both magnitude and direction
of some physical quantity for every point in space.
• In a vector field each point will have magnitude and direction
corresponding to that vector quantity.
𝐸𝐴
q
𝐸𝐵
Fig. 1
Fig. 2
Representation of Vector Field
• A vector field is represented by flux lines known as lines of flow.
• A tangent to these lines at a point gives the direction whereas the
density/length of these lines at any point represent the
strength(magnitude) of the field at that point.
Mathematically
𝐴Ԧ = 𝐴Ԧ (𝑟)
𝐴Ԧ = 𝐴Ԧ (x,y,z)
𝐴Ԧ is a vector quantity
Del operator/Nabla operator( By William Rowan Hamilton (1805-1865).
Also k/as vector differential operator
Clearly, it represents the spatial rate of change of a physical quantity. By itself, it has no
meaning. It assumes a physical meaning only when it is applied to some function.
How it will operate on scalar and vector fields?
φ = gradient of φ= grad φ
. 𝑉 = Divergence of 𝑉 = div 𝑉
X 𝐴Ԧ = Curl of 𝐴Ԧ = Curl 𝐴Ԧ
+= addition operator
d/dx= differentiation operator
∫ dx = integration operator
Gradient of a Scalar function
Consider a x,y,z cartesian coordinate system placed in a
scalar field function associated with every point of a
certain region in space so that it defines a scalar field. Let
A and B be two points in this region having coordinates
(x, y, z) and (x +dx ,y + dy, z + dz) respectively. The position
vectors of A and B
𝑂𝐴 =
𝑂𝐵 =
Let change in φ in going from A to B is dφ , then
1gm of water after a distance of 01 step
…..(iv)
Rate of change= 1gm/step
Total change after 10 steps= 01 gm/step x 10
)
.(
…..(v)
(
)
Φ+dφ
…..(vi)
φ
…..(vii)
is known as gradient of φ and is written as grad φ
Physical significance of Gradient of a scalar
function
Change in the scalar function
Displacement vector
Gradient of scalar function
Gradient of φ is always normal to a level
surface
But dφ =0
Therefore
Angle between
A
=0
And
= 90o
Is normal to a level surface
90o
Level surface
B
dφ=0
Φ= constant
Try some numericals
N1. Find the grad φ at points (0,1,2) where φ = x3y+ xz
N2. Find a unit vector normal to surface x2+ 3y2 + 2z2 + 6 at P(2, 0, 1).
1
N3. Find grad , where 𝑟 = x𝑖Ƹ + y𝑗+Ƹ z𝑘෠
𝑟
N4. Find grad rn , where 𝑟 = x𝑖Ƹ + y𝑗+Ƹ z𝑘෠