A thin wire of infinite extent has a charge per unit length of . Using the cylin

Question

A thin wire of infinite extent has a charge per unit length of . Using the cylindrical Gaussian surface shown in the figure below, it can be shown that the electric field produced by this wire at a radial distance r (where r is in meters) has the following magnitude.

Assume that the electric field at a distance of r = 45.0 cm from the wire has a magnitude of 28,400 N/C.(a) What is the magnitude of the charge per length on this wire?

? C/m

(b) At what distance from the wire is the magnitude of the electric field equal to (1/2)·(28,400 N/C)?

? m

Explanation / Answer

Given that E = /(2 0*r)

For part a) = ?

E = 28400 N/C and r = 45 cm = 0.45 m

then = E*(2 0*r) = 28400*2*3.142*8.85*10^-12*0.45 = 7.1*10^-7 C/m

B) given that E = (1/2)*(28400) = 14200 N/C

r = ?

= 7.1*10^-7 C/m

then r = /(2 0*E) = (7.1*10^-7)/(2*3.142*8.85*10^-12*14200) = 0.899 m = 89.9 cm = 90 cm

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