Why don't electric field lines ever cross each other?

Electric field lines never cross each other because at any point, the electric field has a unique direction.

Electric field lines are a visual tool used in physics to represent the strength and direction of an electric field. The concept of electric field lines was introduced by Michael Faraday, and they are often used to help visualise how electric fields behave. The direction of the field line at a given point indicates the direction of the electric field at that point, while the density of the lines indicates the magnitude of the field.

The reason why electric field lines never cross each other is because the electric field at any point in space is unique. This means that it has a specific magnitude (strength) and direction. If two field lines were to cross, it would imply that the electric field at the point of intersection has two different directions, which is not possible. Therefore, electric field lines are always drawn so that they never intersect.

This principle is not just limited to electric fields, but applies to all types of fields, including gravitational and magnetic fields. It's a fundamental concept in field theory, which is a branch of physics that deals with the study of fields. The idea that field lines never cross is a reflection of the fact that fields themselves are smooth and continuous entities.

In practical terms, this means that if you were to place a small positive test charge at any point in an electric field, it would experience a force that would cause it to move along the direction of the field line passing through that point. If field lines were to cross, the test charge would be faced with a dilemma of choosing which direction to follow, which contradicts the fundamental nature of fields.

In conclusion, the rule that electric field lines never cross each other is a reflection of the fundamental properties of fields, and it helps us to understand and visualise how fields behave.