Unit I
Electromagnetic Theory
Contents
• Del Operator, Gradient, Divergence and Curl
• Gauss’s theorem & Stokes theorem (no proof)
• Law of conservation of charge “Continuity Equation”
• Gauss’ law, Ampere’s Law, Faraday’s Law
• Modified Ampere’s Law, Displacement Current,
• Maxwell’s equations & their Significance
• Poynting vector S
• Poynting Theorem (statement & derivation) & energy dissipation
• E.M.W propagation in free space, dielectrics and conductors
PPT slides presented by: Dr. Pragati Sharma
Applied Physics-I
,Del operator represented by symbol ∇ and expressed as
# # # +
∇= ı̂ + ȷ̂ + k in Cartesian coordinates
#$ #' #)
It is is a vector differential operator and not a vector quantity.
It can operate on any function in three different ways and the result
depends on the manner in which it operates upon the function.
∇ϕ Gradient of a scalar function
∇⋅F Divergence of a vector function
∇×F Divergence of a vector function
All represent the first derivatives 2
,Gradient of a scalar function ∇ϕ
When ∇ operator acts directly upon a scalar function ϕ, the result
is a vector function called Gradient of a scalar function.
#2 #2 #2 +
∇ ϕ = ı̂ + ȷ̂ + k
#$ #' #)
It represents a differential of a scalar function ϕ in 3D space.
Geometrical Significance
It has both magnitude & direction. At the point of gradient, its
magnitude is the slope along the direction of maximum change of
the function with distance & it points along the direction of this
maximum rate of change.
Physical Significance It tells how fast
the function varies with distance. 3
, Laminar or lamellar field
If any vector field A is expressed as gradient of a scalar field, then A
is known as Laminar field e.g. Electrostatic field E is a lamellar field
E=−∇V as it is derived from a scalar potential function V
Q: Find the gradient of ‘r’ or show that ∇r = r7
Where ‘r’ is a distance from the origin O i.e. r= 𝑥 9 + 𝑦 9 + 𝑧 9
P
O
(0,0,0)
4
Electromagnetic Theory
Contents
• Del Operator, Gradient, Divergence and Curl
• Gauss’s theorem & Stokes theorem (no proof)
• Law of conservation of charge “Continuity Equation”
• Gauss’ law, Ampere’s Law, Faraday’s Law
• Modified Ampere’s Law, Displacement Current,
• Maxwell’s equations & their Significance
• Poynting vector S
• Poynting Theorem (statement & derivation) & energy dissipation
• E.M.W propagation in free space, dielectrics and conductors
PPT slides presented by: Dr. Pragati Sharma
Applied Physics-I
,Del operator represented by symbol ∇ and expressed as
# # # +
∇= ı̂ + ȷ̂ + k in Cartesian coordinates
#$ #' #)
It is is a vector differential operator and not a vector quantity.
It can operate on any function in three different ways and the result
depends on the manner in which it operates upon the function.
∇ϕ Gradient of a scalar function
∇⋅F Divergence of a vector function
∇×F Divergence of a vector function
All represent the first derivatives 2
,Gradient of a scalar function ∇ϕ
When ∇ operator acts directly upon a scalar function ϕ, the result
is a vector function called Gradient of a scalar function.
#2 #2 #2 +
∇ ϕ = ı̂ + ȷ̂ + k
#$ #' #)
It represents a differential of a scalar function ϕ in 3D space.
Geometrical Significance
It has both magnitude & direction. At the point of gradient, its
magnitude is the slope along the direction of maximum change of
the function with distance & it points along the direction of this
maximum rate of change.
Physical Significance It tells how fast
the function varies with distance. 3
, Laminar or lamellar field
If any vector field A is expressed as gradient of a scalar field, then A
is known as Laminar field e.g. Electrostatic field E is a lamellar field
E=−∇V as it is derived from a scalar potential function V
Q: Find the gradient of ‘r’ or show that ∇r = r7
Where ‘r’ is a distance from the origin O i.e. r= 𝑥 9 + 𝑦 9 + 𝑧 9
P
O
(0,0,0)
4
