Ampere's law

Magnetic fields, like electric fields, are completely superposable. So, if a field B₁ is generated by a current I₁ flowing through some circuit, and a field B₂ is generated by a current I₂ flowing through another circuit, then when the currents I₁ and I₂ flow through both circuits simultaneously the generated magnetic field is B₁ + B₂.

Consider two parallel wires separated by a perpendicular distance r and carrying electric currents I₁ and I₂, respectively. The magnetic field strength at the second wire due to the current flowing in the first wire is B = μ₀I₁/2πr. This field is orientated at right angles to the second wire, so the force per unit length exerted on the second wire is

 (1.1)

This follows from above as

which is valid for continuous wires as well as short test wires. The force acting on the second wire is directed radially inwards towards the first wire. The magnetic field strength at the first wire due to the current flowing in the second wire is B = μ₀I₂/2πr. This field is orientated at right angles to the first wire, so the force per unit length acting on the first wire is equal and opposite to that acting on the second wire, according to

.

Equation (1.1) is sometimes called ''Ampere's law" and is clearly another example of an ''action at a distance" law; i.e., if the current in the first wire is suddenly changed then the force on the second wire immediately adjusts, whilst in reality there should be a short time delay, at least as long as the propagation time for a light signal between the two wires. Clearly, Ampere's law is not strictly correct. However, as long as we restrict our investigations to steady currents it is perfectly adequate.