Verification of Solenoidal & Irrotational

Math Presentation
Verification of Solenoidal & Irrotational

1. welcome Green university of Bangladesh Md . Al-Amin ID: 172015031 Shakiuzzamn ID: 172015027 Mahabubur Rahim ID: 172015040 Topic : Verification of Solenoidal & Irrotational Department of CSE 1

2. Vector Analysis Vector: A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. Examples of vector quantities displacement, velocity ,  acceleration ,   force, etc. Vector analysis uses, applies and extends the methods of differential and integral calculus to vectors and vector valued functions. The  Dot product,  Cross product,  Scalar multiplication,   Gradient,  Divergence,  Curl , Directional derivative, Stokes ' theorem, Green's theorem , the Divergence theorem, and other mathematical concepts and notions related to vectors are studied within the framework of vector analysis . 2

3. History When and how did vector analysis arise and develop? Vector analysis arose only in the period after 1831 , in the 19th century when  Josiah Willard Gibbs  and  Oliver Heaviside independently developed vector analysis to express the new laws of electromagnetism discovered by the  Scottish  physicist  James Clerk Maxwell . Now three earlier developments deserve attention as leading up to it. These three developments are- T he discovery and geometrical representation of complex numbers. Leibniz’s search for a geometry of position. T he idea of a parallelogram of forces or velocities. 3

4. Solenoidal A vector function is said to Solenoidal on divergence free. That means if div = 0.   Divergence: If v = + is define and differentiable at each point (x,y,z). The divergence of v is define as div v = ∇ . v = + +   4

5. Verification Verifay that , = is Solenoidal or not?   Solution: we know- div = ∇ = + + = ) + + = So f So f is not Solenoidal.   5

6. Irrotational A vector function is said to irrotational on curl free. If curl = o.   Curl: If v = + is define and differentiable at each point (x,y,z). The curl of v is define as- Curl v = ∇ × v =   6

7. Verification Verifay that , = is irrotational or not?   Solution: We know- curl f = ∇ × = = { ( ) ( )} { ( ) – )} + { ( ) ( )} = ( 1+1) ( ) + ( ) = So f is irrotational.   7

8. HAVE ANY QUESTION ? THANK YOU ALL 8