Electric and magnetic fields are regarded as _______

Concept

A physical quantity is classified by how much information is needed to specify it completely. A scalar is fixed by a magnitude with its unit alone and combines by ordinary arithmetic. A vector needs a magnitude and a direction, and combines by the triangle or parallelogram law of vector addition.

Application

Both fields are defined through the force they produce, and force is itself a directed quantity.

1. The electric field at a point is defined as E = F/q0, the force per unit positive test charge. Dividing a directed force by a plain number leaves a quantity that still points somewhere, along the force felt by a positive charge, so E has a direction as well as a magnitude in newton per coulomb (N/C).

2. The magnetic field is defined through the Lorentz force F = qv x B. Stating B requires not only its strength in tesla (T) but also the axis about which the right-hand rule turns v into the force, so B likewise has a direction.

3. When several sources act together, the resultant field is obtained by joining the individual fields head to tail (superposition), not by adding their numbers. Two equal fields pointing opposite ways cancel to zero, a result that adding their magnitudes as plain non-negative numbers could never give.

Cross-check

• Electric potential V, measured in joule per coulomb, is fixed by a single number at each point and needs no direction; that is what a genuinely direction-free field quantity looks like.

• Faraday's law and the Ampere-Maxwell law make a changing magnetic field produce an electric field and a changing electric field produce a magnetic field, and Maxwell's equations treat the two together as one electromagnetic field.

• The fields exert measurable forces on charges and currents, store energy in proportion to E2 and B2, and carry momentum in electromagnetic waves, so they are measurable physical entities.

Electric and magnetic fields therefore carry both magnitude and direction and obey vector addition, so they are regarded as vector quantities.