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.
Table of Contents
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.
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COULOMB’S LAW
Last modified on:3 years agoReading Time:18MinutesCOULOMB’S LAW: Two point electric charges q1 and q2 at rest, separated by a distance r exert a force on each other whose magnitude is given by If between the two charges there is free space then Where ε0 is the absolute electric permittivity of the free space and ε0 =…
