No, electric field lines cannot cross. This is because the electric force on a charged particle depends only on the amount of charge it has and where it is in relation to other charges. The electric force must be perpendicular to both the vector from one charge to another, and also to any line drawn between them. This means that if two electric forces are created at different points and both can be drawn perpendicular to the line between them, then they cannot cross. The following would not work: __ |/\|__||– \__||–| ||-o o–[||] [||] |_ _| Electric field lines never cross because of how the electric force is calculated. This is why when there is an induced current in one wire, a voltage will appear across another nearby wire or bridge as shown below in Figure (a). When this happens, it’s very difficult for electrons to move from one side of a metal surface to the other without crossing through some type of conductor like copper wire which has been cut by
