There is also a law for magnetic fields which says we can represent B (magnetic) fields with vectors. There is a little difference between E and B fields. E fields extend to infinity or until they are absorbed by a particle of opposite polarity. E fields are radiated by positive charged and absorbed by negative charged particles. Magnetic fields form closed loops. There is a three way relation between E fields, B fields, and motion. E fields in motion create B fields. In other words current in a wire will create an electromagnet. A conductor moving in a B field will cause a current to flow in the wire. These factors will always be present perpendicular to each other. We analyze their interactions using vectors. The arrow above the E says use a vector to represent it.
This brings us to the left hand rule for coils.