In the recent thread about demagnetisers someone mentioned welding cables "twitching" when the arc was struck, supposedly because of the interaction between the current in the cable and the Earth’s magnetic field. This seemed unlikely to me, I thought it was more likely to be due to interaction between the cables, so I decided to do some figuring, with the help of formulas in Wikipedia.
The Earth’s magnetic field (according to Wikipedia) varies between 25 and 65 micro Teslas depending where it is measured. The force on L metres of wire due to a current I Amps in a field B Teslas is given by the formula B x I x L Newtons. So the maximum force on 1 metre of cable carrying 100 Amps in the maximum Earth’s field is (if the cable runs E-W perpendicular to the field) 0.0065 Newtons. If the cable was parallel to the field (running N-S) there would be no force.
The “Ampere” force per metre between two parallel wires 1 metre apart each carrying A Amp is 0.0000002 Newton-metres per Amp-squared. The force is given in Newton-metres since it is inversely proportional to wire spacing. So two parallel cables 1 metre apart and carrying 100 Amps have a force between them of 0.000002 x 10,000 = 0.002 Newtons, about a third of that due to the maximum Earth’s field. However if the current was increased to 200 Amps, the force between the wires would be 4x greater; and if the cables are closer together it would be greater still. Another factor is that the Ampere force is in the same direction whether the welding current is DC or AC, whereas the net force in the Earth’s field would be zero for an AC welder.
So it looks like the force in the Earth’s magnetic field is of the same order as the “Ampere force”, depending on the actual current and configuration of the cables. But what’s puzzling is that neither force is very big! A one-kilogram weight exerts a force of 9.81 Newtons, so a Newton is about a tenth of the force exerted when you hold up a bag of sugar (in fact about the weight of an apple). The electromagnetic forces on a metre of welding cable seem to be measurable in apple pips – so why do the cables twitch? Are the peak welding currents much bigger? Or is there some other mechanism at work?