The electric fields
produced by the two elements of the pair when
summed give a resultant electric field which
is radial (the components normal to the radial
vector cancel) This is true for any such pair
and hence the total field at any point P is
radial Finally, since the wire is infinite,
electric field does not depend on the position
of P along the length of the wire In short, the
electric field is everywhere radial in the plane
cutting the wire normally, and its magnitude
depends only on the radial distance r