Question

14.18 Which of the following fields are path independent; surface independent; both; or neither? (a) $y\hat{i} - x\hat{j}$ (d) $xy^2\hat{i} - x^2y\hat{j}$ (b) $\hat{r}$ (e) $\rho z \hat{\phi}$ (c) $-\hat{i}\sin x \cosh y + \hat{j}\cos x \sinh y$

          14.18 Which of the following fields are path independent; surface independent; both; or neither?
(a) $y\hat{i} - x\hat{j}$ 
(d) $xy^2\hat{i} - x^2y\hat{j}$
(b) $\hat{r}$
(e) $\rho z \hat{\phi}$
(c) $-\hat{i}\sin x \cosh y + \hat{j}\cos x \sinh y$

14.18 Which of the following fields are path independent; surface independent; both; or neither?
(a) yî - xĵ
(d) xy^2î - x^2yĵ
(b) r̂
(e) ρ z ϕ̂
(c) -îsin x cosh y + ĵcos x sinh y

Added by Josep G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Zack A

11/12/2023

Step 1

Step 1: To determine if a vector field is path independent, we need to check if the line integral of the vector field along any path between two points is the same. Show more…

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14.18 Which of the following fields are path independent; surface independent; both; or neither? Do path independence only (a) yhat(i)-xhat(j) (b) r (c) -hat(i)sinxcoshy+hat(j)cosxsinhy (d) xy^2hat(i)-x^2yhat(j) (e) ρzhat(ϕ)