Question

Answer the following question.

$(i)$ An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why is it so?
$(ii)$ Explain why two electric field lines never cross each other at any point.

Answer 1

- Hint – In this problem use the concept that the force experienced by a charge is always continuous and don’t has any breakage as the field is continuous, moreover to any point in a field curve depicts the electric field intensity at that point, so use the fact that a single point can’t have two tangents.

Complete step-by-step solution -

$\left( i \right)$ An electrostatic field line is a continuous curve because a charge experiences a continuous force when traced in an electrostatic field (or) it represents the actual path of a unit positive charge, which experiences a continuous force.
The field line cannot have sudden breaks because the charge moves continuously and does not jump from one point to the other.
$\left( {ii} \right)$ If two field lines cross each other at a point, then electric field intensity will show two directions at that point or we can say that because at the point of intersection, two tangents can be drawn to the two lines of force as shown in figure this means two direction of electric field at the point of intersection which is not possible.
Hence, two field lines never cross each other.
As in the diagram field lines cross each other at point A, therefore they will show two directions E1 and E2 as shown in the figure which is not possible.
So this is the required answer.

Note – There are certain other properties of electrostatic fields like they are always perpendicular to the surface charge, in case of positive charge they are radiated outwards however in case of negative charge they are radiated inwards. The field is strong when lines are closer to each other and it is weak when the field lines move apart from each other. The number of field lines is also directly proportional to the magnitude of the charge.