Finding Divergence of Vector Fields on a Sphere

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SUMMARY

The discussion centers on finding the divergence of the vector field F(x,y,z)=(yzi-xzj-xyk)/(x^2 + y^2 + z^2). Participants clarify that substituting (x^2 + y^2 + z^2) with 1 is incorrect, as this simplification does not apply to divergence calculations. The correct approach involves calculating the partial derivatives of each component of the vector field with respect to their respective variables, specifically starting with the derivative of the i component.

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  • Familiarity with partial derivatives
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Students and professionals in mathematics, physics, and engineering who are working on vector calculus problems, particularly those involving divergence in three-dimensional space.

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Hey guys I had a slight problem trying to find divergence of vector fields for the following equation:

F(x,y,z)=(yzi-xzj-xyk)/(x^2 + y^2 + z^2)

So I want to know if its possible of substitute (x^2 + y^2 + z^2) for 1 since that is the equation of a sphere? If not could some one please help me solve this question...Thanks :)
 
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No, you can't put x^2+y^2+z^2 to be 1. You do the problem just like you usually do divergence problems. Start by finding the derivative with respect to x of the i component. So find d/dx y*z/(x^2+y^2+z^2). What do you get?
 
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