conservative field

Let F1, F2, and F3 be functions of (x, y, z). Suppose that for every given pair of points A and B in space, the line integral ∫(F₁dx+ F₂dy + F₃dz) evaluates to the same value along...

Let $F_1$, $F_2$, and $F_3$ be functions of $(x, y, z)$. Suppose that for every given pair of points A and B in space, the line integral $\int\limits_C (F_1 dx + F_2 dy + F_3 dz)$...

The value of the line integral $$\int_P^Q {({z^2}dx + 3{y^2}dy + 2xz\,dz)} $$ along the straight line joining the points $$P(1,1,2)$$ and $$Q(2,3,1)$$ is

Consider the vector field $\overline{\mathbf{F}}=\hat{\mathbf{a}}_{\mathbf{x}}\left(4 y-c_1 z\right)+\hat{\mathbf{a}}_{\mathbf{y}}(4 x+2 z)+\hat{\mathbf{a}}_{\mathbf{z}}(2 y+z)$ in...

Let $$\,\,\,{\rm I} = \int_c {\left( {2z\,dx + 2y\,dy + 2x\,dz} \right)} \,\,\,\,$$ where $$x, y, z$$ are real, and let $$C$$ be the straight line segment from point $$A: (0, 2, 1)...

Consider points $$P$$ and $$Q$$ in $$xy-$$plane with $$P=(1,0)$$ and $$Q=(0,1).$$ The line integral $$2\int\limits_P^Q {\left( {x\,dx + y\,dy} \right)\,\,} $$ along the semicircle...

An electrostatic field is said to be conservative when