Question
a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?
Solution
a) Line of forces are the path of small positive test charge. The charge is moving continuously from point to point rather than jumping from one point to another and experiences continuous force in the electrostatic field. The force experienced, or the path followed by charge cannot be discontinuous and hence the lines are not broken. Also, electrostatic field lines represent the electric field strenth and the strength of field is never broken.
The direction of electric field at a point is displayed by the tangent at that point on a line of force. The direction of electric field line generally changes from point to point and hence are curved lines.
b) In case two electric field lines cross each other then at the point of intersection, we can draw two tangents to the lines of force. And this implies two directions of electric field intensity at the point of intersection, which is not possible.
The direction of electric field at a point is displayed by the tangent at that point on a line of force. The direction of electric field line generally changes from point to point and hence are curved lines.
b) In case two electric field lines cross each other then at the point of intersection, we can draw two tangents to the lines of force. And this implies two directions of electric field intensity at the point of intersection, which is not possible.
Hence, two field lines never cross each other.
