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Just explain to me how this equation was arrived at in boring detail. Thank you orange 1 and 2

Just explain to me how this equation was arrived at in boring detail. Thank you orange 1 and 2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Just explain to me how this equation was arrived at in boring detail. Thank you orange 1 and 2
dx Qy E, 4TE,a (x² + y²)³/2 2 Qy a = 4TE,a y Jy? +a² 1 4TE, yy? +a² 1 4TE,a y 2 y +1 a or 1 EVE? +1 where =2. Here we make a plot of E, /(Q/4TE,a') vs = y/a. a Ey/(Q/4nc0a³) Out[7]= y/a 3.0 0.5 1.0 1.5 2.0 2.5 ((Mathematica))
Transcribed Image Text:dx Qy E, 4TE,a (x² + y²)³/2 2 Qy a = 4TE,a y Jy? +a² 1 4TE, yy? +a² 1 4TE,a y 2 y +1 a or 1 EVE? +1 where =2. Here we make a plot of E, /(Q/4TE,a') vs = y/a. a Ey/(Q/4nc0a³) Out[7]= y/a 3.0 0.5 1.0 1.5 2.0 2.5 ((Mathematica))
Positive charge Q is distributed uniformly along a line with length 2a, lying along the x axis between x = -a and x = a. Find the electric field at point P on the y axis at a distance y. The line charge density is given by å. * x+dx From the symmetry the direction of the electric field is along the y axis. 1 ådx 1 dE, = 2 cos0 %3D 4TE, r? rdx 1 = 2- 4.TE, Jx² + y? y Qy dx 4TE,a (x² + y²)³/2 where r= x² + y? cos 0 = r Jx +y° 2a
Transcribed Image Text:Positive charge Q is distributed uniformly along a line with length 2a, lying along the x axis between x = -a and x = a. Find the electric field at point P on the y axis at a distance y. The line charge density is given by å. * x+dx From the symmetry the direction of the electric field is along the y axis. 1 ådx 1 dE, = 2 cos0 %3D 4TE, r? rdx 1 = 2- 4.TE, Jx² + y? y Qy dx 4TE,a (x² + y²)³/2 where r= x² + y? cos 0 = r Jx +y° 2a
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