Unit-2 EMT Hand Written | Lecture Note

University:
Miami Dade College
Course:
EMS1119 | EMT Lecture
Academic year:

2024
Views:

0

Pages:

17
Author:

Anisha Swain Shah

Electrongnetic unit -II Gauss's Law of Electrostatics Gauss's Law is a fundamental principal in electrostatics that states:- ds "The electric fly through a closed surface is proportional to the net electric charge enclosed by the surface" $.d's = Quet ٤٠ OR The total electric fles through a closed surface is equal to the charge enclosed by the surface. Gauss Law is essential for analyzing electric fields and is used in various areas, from electromagnetic theory to the design of Electric devices. Electric flux: In electromagnetism, electric fly is the total Electric fliefd that line passing through a closed surface Gary Low of Magnetostics: The total magnetic fluys through a closed surface is zero. ds=0 D- oint A vec z d vec s = q/epsilon f = q/L را oint S vec E * d vec J = int V vec nabla * vec EdV q = rho*v q = rho int V dV oint V vec EdV = s epsilon o int V dV oint E ^ * d*nu = int V rho epsilon 0 d nu Rightarrow E Rightarrow rho/epsilon_{0} vec sigma*D = S → D=EE 2 oint S vec B * d vec J = 0 oint S vec B * d vec S = int V vec nabla * vec BdV int V vec a * vec B = 0 vec sigma * vec B = 0 Vector Algebra (calculery) In Vector algebra is the vector differential operates. It is a sort of 3D derivative. It is a mathmatical tool denoted by TA gradient is a terme yed for the differential operator, which is applied to the three dimensioned vector-values function to generate $(x/9/2) scales function of position a vector. 1 gradient divergence - In Vector Calulus divergence is a vector operator that operates on a vector field, a scaler field giving the quantity of the producing vector field's source at each point scalay divergence shows how the field behaves divergence measures the change in density of a orawayfus flowing according to a towards or ar Jud given vector field. froma point, whenas, a curd is used to meaxire the rotational Extent of the field. divergence measure the tendency of the flunt to Collect or disperse at a Maxwell's Syn 1-Differential form:- vec nabla * vec D = S vec D = xi vec E → hams's Law of Electrostatics vec v * vec E = f/epsilon_{0} Blectric Displacement vector f = q/V S Volume charge Density [ii] vec sigma * vec B = 0 →hams's Law of Magnetostatics (ii) vec partial * vec E =- partial vec B partial t سم Faraday's Law [iv] vec partial * vec H = vec J →Amper's Circuital Law x= Mo vec I -> c Current density vec a * vec B = mu 0 vec J + mu 0 partial vec D partial t Modified Maxwell's equ vec partial * vec G = mu 0 vec J + mu n te j vec E dt \rightarrow vec B =A(0 vec J ) , vec g = epsilon* vec E 2- Integral form: oint J vec E * d vec s = 1/epsilon_{0} int V S d vec v [ii] oint 5 vec B * d vec s = 0 in int L vec E vec dJ =- d dt oint S vec B * vec ds [v] int I vec H * d vec I = int S vec J * vec ds Maxwell fourth Cegn is true only for steady state and steady state meowy flows of current is constant far all Fime.

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