Electromagnetic Field Theory: Maxwell's Equations, Waves, and Energy, Lecture notes of Engineering Physics

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Unit – II

Electromagnetic Theory

Dr. Satish Teotia

Assistant Professor

Nims Institute of Engineering and Technology,

Nims University Rajasthan, Jaipur

B. Tech. Physics

UNIT – 2 : Electromagnetic Field Theory Continuity equation for current density, Displacement current, Modifying equation for the curl of magnetic field to satisfy continuity equation, Maxwell’s equations in vacuum and in non-conducting medium, Energy in an electromagnetic field, Poynting vector and Poynting theorem, Plane electromagnetic waves in vacuum and their transverse nature. Relation between electric and magnetic fields of an electromagnetic wave, Energy and momentum carried by electromagnetic waves, Resultant pressure, Skin depth.

NIET Scalar field : A scalar field is defined as that region of space whose each point is associated with scalar function ie. A continuous function which gives the value of a physical quantity like as flux, potential, temperature, etc. (A physical quantity that can be completely described by its magnitude is called a scalar .) Vector field : A vector field is specified by a continuous vector point function having magnitude and direction both changes from point to point in given region of field. The method of presentation of a vector field is called vector line. (A physical quantity having a magnitude as well as a direction is called a vector .)

NIET Gradient , Divergence and curl 4

• The rate of change of scalar and vector fields is denoted by a common operator called Del,or nebla is used which is written as

If^ ^ (x,y,z)^ is^ a^ differentiable^ scalar function, its^ gradient^ is

defined as grad  is a vector whose magnitude at any point is equal to the rate of change of  at a point along a normal tothe surface at the point.

NIET Gauss Divergence theorem (Relation between surface and volume integration )

According to this theorem , the flux of a vector field F⃗ over any closed surface

S is equal to the volume integral of the divergence of the

vector field over the volume enclosed by the surface S.

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NIET Stokes Theorem ( Relation between surface and line integration)

• The surface integral of the curl of a vector field A⃗ (^) taken over an surface S is equal to the line integral of A⃗ around the closed curve. 8

NIET Continued…………….. 10

By the law of conservation of charge i.e. "Charge can neither be created nor destroyed". If some charge flows out from the volume per unit time giving rise to current density, the charge in the volume decreases at the same rate. So the current

Displacement current

Maxwell propose the idea of displacement current. According to

Maxwell, the magnetic fields are not only due to circulating

currents but also due to time dependent changes in the electric

field. Hence this type of time varying field is equivalent to a

current called displacement current.

Consider a parallel trade capacitor connected to a battery as

shown in the figure.

Displacement current

From equation (2), it is evident that rate of change of displacement

vector is equivalent to a current density. It is called displacement

current density. It is equal to the density of current flowing in the

outer circuit.

Maxwell’s Equations