Manipulating Equations with Del Operators

A and B has a zero divergence, then it can be written as the curl of another vector field. However, if E has a non-zero divergence, then it cannot be written as the curl of another vector field. In summary, the divergence of a vector field can be cancelled if it has a zero divergence, but not if it has a non-zero divergence.
  • #1
dm164
21
1
I'm trying to understand how to manipulate equations with del operators.

If I have a equation like :

div( A + B ) = div(E)
and assume A,B,E are twice differential vectors

do div cancel?

can I say E = A + B?

If I write is like this
div( A + B - E ) = 0
div( A + B - (A + B)) = 0
div( 0 ) = 0.

but div( constant ) = 0 also
 
Physics news on Phys.org
  • #2
Look at examples of vector fields that are constant. A+B might be one constant field with a zero divergence and E might be a different one.
 
  • #3
dm164 said:
I'm trying to understand how to manipulate equations with del operators.

If I have a equation like :

div( A + B ) = div(E)
and assume A,B,E are twice differential vectors

do div cancel?

can I say E = A + B?

if the divergence of a vector field is zero then it is the curl of another vector field.
 

What is a del operator?

A del operator, also known as a gradient operator, is a mathematical symbol used to represent the vector operation of taking the gradient of a scalar field.

How do I use a del operator?

To use a del operator, you must first identify the scalar field that you want to take the gradient of. Then, you can apply the del operator to the scalar field by multiplying it to the right of the field. The result will be a vector field.

What are the common del operators used in equations?

The most common del operators used in equations are the gradient (∇), divergence (∇·), and curl (∇×) operators. These operators are frequently used in vector calculus and are useful for solving equations in physics and engineering.

Can del operators be used in multiple dimensions?

Yes, del operators can be used in multiple dimensions. In fact, they are most commonly used in three-dimensional space, but can also be applied in two or more dimensions. In higher dimensions, the del operator becomes more complex and involves partial derivatives.

What are some real-world applications of del operators?

Del operators have many real-world applications, such as in fluid mechanics, electromagnetism, and heat transfer. They are used to describe and solve equations related to these fields, such as the Navier-Stokes equations in fluid mechanics and Maxwell's equations in electromagnetism.

Similar threads

Div and curl in other coordinate systems
    • Calculus
Replies
2
Views
1K
JavaScript Why use spread operator when sorting an array in JavaScript?
    • Programming and Computer Science
Replies
2
Views
1K
Making sense of vector derivatives
    • Calculus
Replies
2
Views
1K
I Inverse Laplace transform of a rational function
    • Calculus
Replies
2
Views
1K
Questions on conditions for calculating flux integrals?
    • Calculus
Replies
1
Views
1K
I Divergence of first Piola-Kirchoff stress tensor
    • Classical Physics
Replies
1
Views
607
C/C++ Errors trying to compile a simple code
    • Programming and Computer Science
Replies
22
Views
2K
I Order of Operations for Tensors
    • Calculus
Replies
1
Views
1K
A Steady state confined flow field: Is it cyclic?
    • Classical Physics
Replies
9
Views
951
Using Euler's Formula to write a fraction in another form
    • Precalculus Mathematics Homework Help
Replies
12
Views
2K

Hot Threads

Recent Insights

Back
Top