PPT-DIVERGENCE & CURL OF B; STOKES THEOREM

Class Activities Stokes Thm Div Curl Ampere 1 Class Activities Stokes Thm Div Curl Ampere 2 Amperian loop analysis Consider the infinite uniform current sheet K flowing in the x direction. The integral is performed through the volume where the currents are but as usual we can extend th eintegraltoallspaceforfreesincewhere is zero the contribution to the integral vanishes anyway Before starting computing derivatives let s be totally ex So if PQR then div 8711 8706x 8706y 8706z PQR 8706P 8706x 8706Q 8706y 8706R 8706z Notice that div is a scalar Find div for each of the following vector 64257elds i xyyzxz ii yzxzxy iii where iv grad where is a function with continuous second der e is identi64257ed with the vector that is obtained by translating to the point Thus every vector 64257eld on is uniquely determined by a function from Ra64257kul Alam IITG MA102 2013 brPage 3br Vector Fields Curl and Divergence Examples of vector 3 Examples of Stokes Theorem Given the vector 64257eld 4 ye xe 2 ze verify Stokes theorem for the hemispherical surface with z 0 Over the hemisphere and we have already shown that dS sin 952d952d966e integrals. Line . integrals. Surface. . integrals. Volume. . integrals. Integral . theorems. The. . divergence. . theorem. Green’s. . theorem. in . the. . plane. Stoke’s. . theorem. Conservative. inCurvilinearCoordinates Althoughcartesianorthogonalcoordinatesareveryintuitiveandeasytouse,itisoftenfoundmoreconvenienttoworkwithothercoordinatesystems.Beingabletochangeallvariablesandexpressioninvol COORDINATE SYSTEMS. . RECTANGULAR or Cartesian. . CYLINDRICAL. SPHERICAL. Choice is based on symmetry of problem. Examples:. Sheets - RECTANGULAR. Wires/Cables - CYLINDRICAL. Spheres - SPHERICAL. . SEM : 3. rd. . BATCH : B-5. presentation by : . . maheta. . dhrati. . (. 140433111017). . TOPIC:DIVERGENCE. . THEORAM. DEFINATION:. “The integral of the normal component of a vector function over a closed surface equals the integral of the divergence of that vector throughout the volume v enclosed by the surface s’’. Integrability. . in Non-critical String/M Theory. (and in the Multi-cut Matrix Models. ). Hirotaka. . Irie. . (Yukawa Institute for Theoretical Physics). May . 17. th. . 2012 . @ . Nagoya Univ.. Preclass0. Yes, I do!. Do you have an Iclicker to use for this term?. Press & HOLD power (blue light . flashes). Key in . AB. (OUR code for this room). Brief green Status flash confirms! . (Blue light steady). Divergence. In calculus, the divergence is used to measure the magnitude of a vector field’s source or sink at a given point. Thus it represents the volume density of the outward flux of a vector field . Week 2. Vector Operators. Divergence and . Stoke’s. Theorems. Gradient Operator. The gradient is a vector operator denoted . . . and sometimes also called “del.” It is most often applied to a real function of three variables. . . RECTANGULAR or Cartesian. . CYLINDRICAL. SPHERICAL. Choice is based on symmetry of problem. Examples:. Sheets - RECTANGULAR. Wires/Cables - CYLINDRICAL. Spheres - SPHERICAL. To understand the Electromagnetics, we must know basic vector algebra and coordinate systems. So let us start the coordinate systems.. Stokes's. theorem: . The . curl . of . A . is the rotational vector whose magnitude is the maximum circulation of A per unit area as the area tends to zero and whose direction is the normal direction of the area when the area is oriented so as to make the circulation maximum..