(a) Determine which of the following vector fields could be electrostatic by computation of the curl for each one. (1) E = k(xyx + 2yzÿ + 3xz2) (ii) E = k(v²&+ (2xry +z')ŷ+2yzî) (b) Since electrostatic fields are conservative, the potential difference between two points is independent of the path taken when evaluating the line integral of the electric field. For the electrostatic field you found in part (a), determine the potential difference between an arbitrary point (xo, yo, zo) and the origin by calculating the line integral along the path described below. That is, use the fundamental theorem of gradients to find V(x,Vo:-a)–V(0,0,0) = - |Ē-dī The starting point is at the origin and the path takes three straight-line steps, each parallel to a coordinate axis, to get to the endpoint: (0,0,0) → (Xo,0,0) → (Xo, yo,0) → (Xo, yo, Zo)

(a) Determine which of the following vector fields could be electrostatic by computation of the curl for each one. (1) E = k(xyx + 2yzÿ + 3xz2) (ii) E = k(v²&+ (2xry +z')ŷ+2yzî) (b) Since electrostatic fields are conservative, the potential difference between two points is independent of the path taken when evaluating the line integral of the electric field. For the electrostatic field you found in part (a), determine the potential difference between an arbitrary point (xo, yo, zo) and the origin by calculating the line integral along the path described below. That is, use the fundamental theorem of gradients to find V(x,Vo:-a)–V(0,0,0) = - |Ē-dī The starting point is at the origin and the path takes three straight-line steps, each parallel to a coordinate axis, to get to the endpoint: (0,0,0) → (Xo,0,0) → (Xo, yo,0) → (Xo, yo, Zo)

Name: Please answer (a), (b), and (c), showing all work. (c) In the end, not
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Description: Please answer (a), (b), and (c), showing all work. (c) In the end, note that the field point chosen is arbitrary, so that you have really found theelectrostatic potential field, relative to the reference point at the origin, that isV(xo, yo, zo) = V(

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Please answer (a), (b), and (c), showing all work.

(c) In the end, note that the field point chosen is arbitrary, so that you have really found the
electrostatic potential field, relative to the reference point at the origin, that is
V(xo, yo, zo) = V(x, y, z).
Check your answer to part (b) by calculating the gradient VV(x,y,z).

(a) Determine which of the following vector fields could be electrostatic by computation
of the curl for each one.
(i) E = k(xyx + 2yzŷ + 3xzż)
(ii) E = k(y³&+ (2xy + z')ŷ + 2yz2)
(b) Since electrostatic fields are conservative, the potential difference between two points is
independent of the path taken when evaluating the line integral of the electric field.
For the electrostatic field you found in part (a), determine the potential difference
between an arbitrary point (xo, yo, zo) and the origin by calculating the line integral along
the path described below. That is, use the fundamental theorem of gradients to find
V(x,yo;70.)-V(0,0,0) =- Ē- di
E
The starting point is at the origin and the path takes three straight-line steps, each parallel
to a coordinate axis, to get to the endpoint:
(0,0,0) →
> (Хо,0,0) —> (Хо, уо,0) —> (Хо, Уо, Zo)

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