Vector calculus - line integral

In summary, the conversation discusses finding the work done by an inverse square force field, represented by F(r) = cr/|r|^{3}, in moving an object from point P1 to point P2. The distances d1 and d2 from these points to the origin are also mentioned. It is suggested to start by finding the integral of F with respect to dr, and to consider using a potential function to derive the vector field.
  • #1
braindead101
162
0
Suppose that F is an inverse square force field; this is, F(r) = cr/ |r|[tex]^{3}[/tex] for some constant c, where r = xi + yj + zmbfk. Find the work done by F in moving an object from a point P1 along a path to a point P2 in terms of the distances d1 and d2 from these points to the origin.

Not exactly sure where to start, do i still find the integral of F with respect to dr..., and there's no r(t).. like other questions, so i am lost.
 
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  • #2
Your vector field can be derived from a potential function. Start there.
 

What is a line integral in vector calculus?

A line integral in vector calculus is a type of integral that is used to calculate the total value of a vector field along a specific curve or path. It takes into account both the magnitude and direction of the vector field.

What is the difference between a line integral and a regular integral?

A regular integral is used to find the area under a curve, while a line integral takes into account the direction of the curve and the vector field. It is also calculated along a specific path rather than over a region.

How is a line integral calculated?

A line integral is calculated by dividing the curve into small segments, finding the value of the vector field at each segment, and then summing up the products of the value and the length of each segment. This is then approximated as the curve becomes infinitely small.

What is the significance of line integrals in physics?

Line integrals are used in physics to calculate quantities such as work, flux, and circulation. They are also used in electromagnetic theory to calculate the electric and magnetic fields.

What are some real-world applications of line integrals?

Line integrals have many real-world applications, including calculating the work done by a force along a curved path, finding the flow of a fluid through a curved pipe, and calculating the electric potential along a wire or circuit.

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