To calculate result you have to disable your ad blocker first.
Choose divergence or curl, enter the values, and hit the calculate button to find the divergence or curl.
Divergence calculator is used to finding the divergence of the given vector field with steps in no time.
What is a divergence of a function?
The divergence of a vector is a method that turns a vector field into a scalar value. We obtain the scalar field by differentiating the given vector field. It is also known as the dot product of a vector field with the nabla operator.
Formula of divergence:
A vector field F(x, y, z) and the nabla operator ∇=(∂/∂x, ∂/∂y, ∂/∂z). Then the divergence of the vector will be
div. F = ∇.F = ∂/∂x(F(x,y,z)) + ∂/∂y(F(x,y,z)) + ∂/∂z(F(x,y,z))
Explanation of the divergence:
The divergence of the function may be positive, negative, or zero. Let F is a vector
- If ∇. F < 0; it means the divergence is negative which identifies the fluid is denser at the given point.
- If ∇. F > 0; it means the divergence is positive which identifies the fluid is less dense at the given point.
- If ∇. F = 0; it means the divergence is zero which identifies the density of the fluid as constant at a given point.
How do we get the divergence?
To understand the step-by-step solution, we have discussed an example below comprehensively.
Find the divergence of the function (cos(xyz), x2, z3) at the point (2, 3, 4).
Step 1: It is the dot product of ∇=(∂/∂x, ∂/∂y, ∂/∂z) with the function.
∇.(cos(xyz), x2, z3)
Step 2: Now calculate the partial derivative of the function.
∂/∂x(cos(xyz)) = -yz sin(xyz)
∂/∂y(x2) = 0
∂/∂z(z3) = 3z2
Step 3: Combine the terms.
∇.(cos(xyz), x2, z3) = -yzsin(xyz)+ 3z2
Step 4: Put the value of the terms in the above function.
= -3(4)sin((2)(3)(4))+ 3(4)2