A uniform line charge extends from x = - 2.6 cm to x = + 2.6 cm and has a linear

Question

A uniform line charge extends from x = - 2.6 cm to x = + 2.6 cm and has a linear charge density of 6.3 nC/m.

(a) Find the total charge. --> it's 0.33 (I got this answer correct)

Find the electric field on the y axis at the following distances.
(b) when y = 4 cm ----> ______N/C

(c) when y = 12 cm -----> ______N/C

(d) when y = 4.5 m ----> 0.146 N/C (I got this answer correct)

(e) Find the field at y = 4.5 m, assuming the charge to be a point charge
0.146 N/C (I got this answer correct)

Please do pay attention on the UNITS!!
It's only two problem!!! (b) and (C)!!!

Explanation / Answer

= 6.3 nC/m, dq = dx, b = 2.6 cm
dE = k dq/(x2 + y2)
dEy = k dq*y/(x2 + y2)3/2
E = -bb k dq*y/(x2 + y2)3/2 = ky -bb 1/(x2 + y2)3/2 dx = ky * x/[y2 (x2 + y2)]|-bb
= 2kb/[y (b2 + y2)] = 2.95/[y (0.0262 + y2)]
y = 4 cm, E = 2.95/[0.04 (0.0262 + 0.042)] = 1.55*103 N/C
y = 12 cm, E = 2.95/[0.12 (0.0262 + 0.122)] = 200 N/C

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