PPT-Del operator Part II Curl of a vector and

Stokess 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. By de64257nition if M then the two dimensional curl of is curl Example If x y then x y and so curl 1 x y Notice that x is vector valued function and its curl is scalar valued function It is important that we label this as the two dimensional curl 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 By the way the gradient of isnt always denoted sometimes its denoted grad As you know the gradient of a scalar eld is f x f x f x We can abstract this by leaving out the to get an operator x x x which when applied to yields This is called t 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 LOOSE CURLS 8 or 1 MEDIUM C URLS 10 TIGHT C URLS 10 o r 12 CURL T YPE TIME Loose Curls Medium Curls Ti ght Curls Curl cret Fast easy fabulous brPage 3br 11 FEATURES 1 Ceramic tourmaline curl chamber 2 Power on and temperature settings 3 Temperature LECTURE - 24- CURL OF A VECTOR FIELD. [Chapter – 8.11]. DEPARTMENT OF MATHEMATICS, CVRCE. DEFINITION OF CURL. AN EXAMPLE ON CURL. Example:. Find the curl of . Class Activities: Vector Potential. One of Maxwell’s equations, made it useful for us to define a scalar potential V, where . . . Similarly, another one of Maxwell’s equations makes it useful for us to define the vector potential, . COORDINATE SYSTEMS. . RECTANGULAR or Cartesian. . CYLINDRICAL. SPHERICAL. Choice is based on symmetry of problem. Examples:. Sheets - RECTANGULAR. Wires/Cables - CYLINDRICAL. Spheres - SPHERICAL. 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). 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. . pUC 1 18 Product Information Sheet # V333 02 MoBiTec GmbH, Germany Phone: +49 551 70722 0 Fax: +49 551 70722 22 E - Mail: info@mobitec.com www.mobitec.com Revised January 2014 1 Product p UC 1 18 Class Activities: Potential (slide 2). Today: Voltage or “Electric Potential”. The 1120 version:. Voltage V = . kq. /r from a point charge. Voltage = potential energy/charge. D. V is “path independent”. . 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..