Question

Determine whether each of the following vector fields appears to be path independent (conservative) or path dependent (not conservative).

Answer 1

A vector field is considered path independent, or conservative, if the work done by the field when moving between two points is the same regardless of the path taken. To determine if a vector field is conservative, we can apply the condition stated in Equation 8.10, which involves using the derivatives of the components of the force.

Step-by-step explanation:

A vector field is considered path independent, or conservative, if the work done by the field when moving between two points is the same regardless of the path taken. On the other hand, a vector field is path dependent, or non-conservative, if the work done depends on the path taken. To determine if a vector field is conservative, we can apply the condition stated in Equation 8.10, which involves using the derivatives of the components of the force. If the derivative of the y-component of the force with respect to x is equal to the derivative of the x-component of the force with respect to y, then the force is conservative. If the derivatives are not equal, the force is non-conservative.