5. Hayt (9th edition): Problem 2.27Given the electric field E = (4x – 2y)âx – (2x + 4y)ây, find--(a) the equation of the streamline that passes through the point P(2,3, –4).(b) a unit vector specifying the direction of E at Q(3,–2,5).

Part (a): The given expression is rewritten as given below: E→x=4x-2ya^x…

Answered: 5. Hayt (9th edition): Problem 2.27…

Introductory Circuit Analysis (13th Edition)

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ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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5. Hayt (9th edition): Problem 2.27
Given the electric field E = (4x – 2y)âx – (2x + 4y)ây, find
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(a) the equation of the streamline that passes through the point P(2,3, –4).
(b) a unit vector specifying the direction of E at Q(3,–2,5).

Expert Solution

Step 1

Part (a):

The given expression is rewritten as given below:

${\vec{E}}_{x} = (4 x - 2 y) {\hat{a}}_{x} \dots (1) {\vec{E}}_{y} = - (2 x + 4 y) {\hat{a}}_{y} \dots (2)$

Divide equation (1) by equation (2),

$\frac{{\vec{E}}_{x}}{{\vec{E}}_{y}} = \frac{(4 x - 2 y)}{- (2 x + 4 y)} \frac{(4 x - 2 y)}{- (2 x + 4 y)} = \frac{d x}{d y} (4 x - 2 y) d y = - (2 x + 4 y) d x 4 x d y - 2 y d y = - 2 x d x - 4 y d x 4 (x d y + y d x) = 2 y d y - 2 x d x 4 (d x y) = d y^{2} - d x^{2} [d (x y) = x d y + y d x d y^{2} = 2 y d y d x^{2} = 2 x d x]$

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