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 = 5.7 nC/m.
a) find total charge: .2964
Find the electric field on the y axis at the following distances.
(b) y = 4 cm
c) y = 12 cm
(d) y = 4.5 m
e) Find the field at y = 4.5 m, assuming the charge to be a point charge

Explanation / Answer

q = 5.7 nC/m Total length = 5.2 cm = 0.052 m a) Q = q*0.052 = 0.2964 nC/m dQ = qdx As r = square root of (y^2 + x^2) dE = k dQ / (y^2 + x^2) ==> E = kq * integral of dx/(y^2 + x^2) from x = -0.026 to 0.026 L E = kq*[(1/y) tan-1 (x/y)] from x = -0.026 to 0.026 = 51.3*[(1/y) tan-1 (x/y)] from x = -0.026 to 0.026 b)Now for y = 0.04 m, E = 1478.4 N/C c)For y = 0.12 m, E = 182.43 N/C d)For y = 4.5 m, E = 0.13173 N/C e)Considering point charge E = kQ/4.5^2 = 0.13173 N/C

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