An infinitely long thin wire carries a uniform charge per unit length #q#. Find the electric field at a distance of #R# units from the wire?

1 Answer
Jan 29, 2017

Answer:

Electric field is #q/(4epsilon_0R)#, where #q# is the uniform charge per unit length and #epsilon_0# is electrical permittivity of free space

Explanation:

Consider the infinitely long thin wire to carry a uniform charge per unit length #q#,
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The field created by a small portion #dx# of it at a distance #R# will be

#1/(4piepsilon_0)xx(qdx)/sqrt(x^2+R^2)#, where #epsilon_0# is electrical permittivity of free space

and total field created by thin wire will be

#1/(4piepsilon_0)int_(-oo)^(oo)(qdx)/sqrt(x^2+R^2)#

= #q/(4piepsilon_0)int_(-oo)^(oo)(dx)/sqrt(x^2+R^2)#

= #q/(4piepsilon_0)1/R|tan^(-1)(x/R)|_(-oo)^(oo)#

= #q/(4piepsilon_0R)(pi/2-(-pi/2))#

= #q/(4epsilon_0R)#