Question

Why do electric field lines never cross?

Short answer

Answer: Electric field lines never cross because the electric field is unique at any point in space. Crossing field lines would imply that there is more than one value of electric field intensity at a given point, violating the fundamental laws of physics. This would lead to ambiguous conclusions about the direction and magnitude of the force acting on a charged particle at that location.

Step-by-step solution

Understanding the electric field

The electric field is a vector field, which means that at every point in space, there is an electric field vector associated with it. This vector represents the force experienced by a unit positive charge if it were placed at that point. That means the direction of the vector represents the direction of the force on the charge, and its magnitude represents the strength of the force.

Defining electric field lines

Electric field lines are a visual representation of how electric charge would influence the space around it. The lines are drawn so that the tangent to the line at any point represents the direction of the electric field at that point. The spacing of the lines is also significant; denser field lines indicate a stronger electric field, whereas sparser lines indicate a weaker field.

Explaining the uniqueness of electric field direction

The main reason electric field lines never cross is because of the uniqueness of the electric field direction at any point in space. If electric field lines were to cross, there would be two different electric field vectors (meaning two different directions) at that location. This would mean that a charged particle placed at the point of intersection would experience two different simultaneous forces, which is contradictory to the concept of electric field - the field acts with one unique force on the charge at that given point.

Visualizing the field lines of multiple charges

When we have more than one charge present, the total electric field at a point is the vector sum of the individual electric fields created by each charge. Although the individual field lines may appear to come close to each other, they essentially reshape themselves in response to the total electric field vector, ensuring that the lines never actually cross.

Understanding the consequences of crossing field lines

If electric field lines were to cross, it would imply that there is more than one value of electric field intensity at a given point in space, violating the fundamental laws of physics that state the electric field is unique at any point in space. This would lead to ambiguous conclusions about the direction and magnitude of the force acting on a charged particle at that location. In conclusion, electric field lines never cross because the electric field is unique at any point in space, and the lines serve as a visual representation of the direction and magnitude of the force on a charged particle at any given location.