Vector field equation - Find work of the field

In summary, the conversation is about finding the potential equation for a given vector field and using it to calculate the work of the field along a given path. The speaker suggests plugging in the start and end points of the path into the potential equation to find the work. The other person agrees and mentions that the question seemed easy and they received a high score on it. Overall, the conversation ends on a positive note with the other person expressing their satisfaction with the speaker's help.
  • #1
asi123
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0

Homework Statement



I have this vector field equation, the first part of the question is to find the potential equation for it, I found it.
The second part of the question is to find the work of the field through this path.
My idea is to plug t in the r equation, because I'm not sure but I think (x,y,z)=(component of r), is that right? and that way I find the start point of the path and the end point, plug it into the potential equation and that's it, is that right?

Homework Equations





The Attempt at a Solution

 

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  • #2


Sure, that's it.
 
  • #3


Dick said:
Sure, that's it.

10x, it seemed so easy, and they gave 10 points for it (it's a question from a test), so I got confuse...
 
  • #4


Well done! I didn't have to help much, did I? I like that.
 

1. What is a vector field equation?

A vector field equation is a mathematical expression that describes the behavior of a vector field, which is a quantity that has both magnitude and direction. It is commonly used in physics and engineering to model physical phenomena such as fluid flow or electrical fields.

2. How do you find the work of a vector field?

The work of a vector field is found by integrating the dot product of the vector field and a path over which the field is acting. This involves multiplying the magnitude of the field at each point along the path by the distance traveled along the path, and then summing these values together.

3. What is the significance of finding the work of a vector field?

The work of a vector field is a measure of the energy that is transferred when a force is applied over a certain distance. It can be used to understand and predict the behavior of physical systems, such as the motion of particles in a fluid or the movement of charged particles in an electric field.

4. How is the work of a vector field related to potential energy?

The work of a conservative vector field, which is one that does not depend on the path taken, is equal to the change in potential energy between two points. This means that if the work of a vector field is known, we can calculate the potential energy at any point within the field.

5. Are there any real-world applications of vector field equations?

Yes, vector field equations have many real-world applications, such as in fluid dynamics, electromagnetism, and climate modeling. They can be used to understand and predict the behavior of complex systems, and are essential in many fields of science and engineering.

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