Electric Field of a Line Charge

Electric Field of a Line Charge

Positive charge q is distributed uniformly along a line with length 2a, lying along the y-axis between y=–a and y=+a. We are here interested in finding the electric field at point P on the x-axis.

Derivation of electric field due to a line charge:

Thus, electric field is along x-axis only and which has a magnitude,

From the above expression, we can see that

(i) If x>>a, Ex=kq/x², i.e. if point P is very far from the line charge, the field at P is the same as that of a point charge.

(ii) if we make the line of charge longer and longer, adding charge in proportion to the total length so that λ, the charge per unit length remains constant.

Thus, the magnitude of electric field depends only on the distance of point P from the line of charge, so we can say that at any point P at a perpendicular distance r from the line in any direction, the field has magnitude

Graph:

Variation of electric field with distance is shown in the figure.

The direction of E is radially outward from the line.