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Almost exactly 200 years ago, Ørsted discovered that a compass needle pointed along circular paths around a current-carrying wire. Shortly afterwards, Ampère found that two wires carrying currents in the same direction attract each other. Whereas Ampère saw the phenomenon as action-at-a-distance between the wires, the notion of field-as-agent came to supersede action-at-a-distance. Ørsted's compass was now seen as giving the direction of the field due to a wire, and the force on each of Ampère's current-carrying wires was seen as being at right angles to the wire and to the (causative) field due to the other wire. That the force is at right angles to the plane containing the magnetic field and current density vectors was confirmed and generalised by further experiments.

The names 'cross product' or 'vector product', and the vector algebra notation, to describe such a relationship came later. The experimental findings helped to motivate the mathematical concept, not the other way round. And, of course, it wasn't just electromagnetism that gave rise to the cross product idea. Torque and angular momentum cry out for the treatment.

Almost exactly 200 years ago, Ørsted discovered that a compass needle pointed along circular paths around a current-carrying wire. Shortly afterwards, Ampère found that two wires carrying currents in the same direction attract each other. Whereas Ampère saw the phenomenon as action-at-a-distance between the wires, the notion of field-as-agent came to supersede action-at-a-distance. Ørsted's compass was now seen as giving the direction of the field due to a wire, and the force on each of Ampère's current-carrying wires was seen as being at right angles to the wire and to the (causative) field due to the other wire. That the force is at right angles to both the magnetic field and current density vectors was confirmed and generalised by further experiments.

The names 'cross product' or 'vector product', and the vector algebra notation, to describe such a relationship came later. The experimental findings helped to motivate the mathematical concept, not the other way round. And, of course, it wasn't just electromagnetism that gave rise to the cross product idea. Torque and angular momentum cry out for the treatment.

Almost exactly 200 years ago, Ørsted discovered that a compass needle pointed along circular paths around a current-carrying wire. Shortly afterwards, Ampère found that two wires carrying currents in the same direction attract each other. Whereas Ampère saw the phenomenon as action-at-a-distance between the wires, the notion of field-as-agent came to supersede action-at-a-distance. Ørsted's compass was now seen as giving the direction of the field due to a wire, and the force on each of Ampère's current-carrying wires was seen as being at right angles to the wire and to the (causative) field due to the other wire. That the force was at right angles to the plane containing the field and current density vectors was confirmed and generalised by further experiments.

The names 'cross product' or 'vector product', and the vector algebra notation, to describe such a relationship came later. The experimental findings helped to motivate the mathematical concept, not the other way round. And, of course, it wasn't just electromagnetism, that gave rise to the cross product idea. Torque and angular momentum cry out for the treatment.

Almost exactly 200 years ago, Ørsted discovered that a compass needle pointed along circular paths around a current-carrying wire. Shortly afterwards, Ampère found that two wires carrying currents in the same direction attract each other. Whereas Ampère saw the phenomenon as action-at-a-distance between the wires, the notion of field-as-agent came to supersede action-at-a-distance. Ørsted's compass was now seen as giving the direction of the field due to a wire, and the force on each of Ampère's current-carrying wires was seen as being at right angles to the wire and to the (causative) field due to the other wire. That the force is at right angles to the plane containing the magnetic field and current density vectors was confirmed and generalised by further experiments.

The names 'cross product' or 'vector product', and the vector algebra notation, to describe such a relationship came later. The experimental findings helped to motivate the mathematical concept, not the other way round. And, of course, it wasn't just electromagnetism that gave rise to the cross product idea. Torque and angular momentum cry out for the treatment.

Almost exactly 200 years ago, Ørsted discovered that a compass needle pointed along circular paths around a current-carrying wire. Shortly afterwards, Ampère found that two wires carrying currents in the same direction attract each other. Whereas Ampère saw the phenomenon as action-at-a-distance between the wires, the notion of field-as-agent came to supersede action-at-a-distance. Ørsted's compass was now seen as giving the direction of the field due to a wire, and the force on each of Ampère's current-carrying wires was seen as being at right angles to the wire and to the (causative) field due to the other wire. This was confirmed and generalised by further experiments.

The names 'cross product' or 'vector product', and the vector algebra notation, to describe such a relationship came later. The experimental findings helped to motivate the mathematical concept, not the other way round. And, of course, it wasn't just electromagnetism, that gave rise to the cross product idea. Torque and angular momentum cry out for the treatment.

Almost exactly 200 years ago, Ørsted discovered that a compass needle pointed along circular paths around a current-carrying wire. Shortly afterwards, Ampère found that two wires carrying currents in the same direction attract each other. Whereas Ampère saw the phenomenon as action-at-a-distance between the wires, the notion of field-as-agent came to supersede action-at-a-distance. Ørsted's compass was now seen as giving the direction of the field due to a wire, and the force on each of Ampère's current-carrying wires was seen as being at right angles to the wire and to the (causative) field due to the other wire. That the force was at right angles to the plane containing the field and current density vectors was confirmed and generalised by further experiments.

The names 'cross product' or 'vector product', and the vector algebra notation, to describe such a relationship came later. The experimental findings helped to motivate the mathematical concept, not the other way round. And, of course, it wasn't just electromagnetism, that gave rise to the cross product idea. Torque and angular momentum cry out for the treatment.