(a) An infinitely long thin straight wire has a uniform linear charge density \lambda. Obtain the expression for the electric field (E) at a point lying at a distance x from the wire, using Gauss’ law.

(b) Show graphically the variation of this electric field E as a function of distance x from the wire.

 

 
 
 
 
 

Answers (1)

a) Consider an infinity long straight conductor of linear charge density \lambda

Consider a cylindrical Gaussian surface of radius x and length l.
charge enclosed by the surface
q= \lambda l
By Gauss law
\oint \vec E\cdot ds= \frac{q}{\varepsilon _{0}}= \frac{\lambda l}{\varepsilon _{0}}
\vec E\oint ds= \frac{\lambda l}{\varepsilon _{0}}
\vec E\times 2\pi xL= \frac{\lambda L}{\varepsilon _{0}}
E= \frac{\lambda }{2\pi x\varepsilon _{0}}

b)

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