The interaction of currents is very well known in modern electrical engineering: it is taken into account when designing complex nuclear reactors of the Tokamak type and in the design of electric motors. For example, in the latter there is a shift of nearby turns of the stator winding to the rotor winding. So, during the “heavy” start-up of powerful machines, when the current reaches the maximum permissible values, damage to the winding holding wires can be observed. In this case, there is a magnetic interaction of currents flowing through two different windings. Their rotating magnetic fields have an attractive effect on the conductors. When studying the interaction of currents, it is usually the magnetic type of interaction that is considered, although in fact this topic is more extensive.
Imagine a three-phase network, each line of which has its own group of consumers. While their total resistances are approximately equal, the whole system works stably, but if the current balance is substantially disrupted, a regime called “phase imbalance” sets in, which can damage the equipment. Also, the interaction of currents occurs when several power sources are connected at the same load in parallel. In this case, if the phasing is performed correctly, the current flows between the sources (for a short time, for example), but if the phase lines do not match, a short circuit is obtained. Obviously, the interaction of currents manifests itself in different ways. Nevertheless, it is most commonly accepted to consider Ampere's Law.
If between the opposite poles of a magnet (a constant magnetic field) a moving frame is placed through which current flows, then it will rotate at a certain angle determined by the strength of the interaction of the two magnetic fields and the direction of the tension lines. This force was defined and formulated in 1820 by the famous French physicist A.M. Ampère.
Currently, the following formulation is used: when a current flows through a thin section conductor located in a magnetic field, the force dF that affects a certain section (dl) of the wire is directly dependent on the current strength I and the vector product of the length dl and the magnetic induction value B. That is:
dF = (I * dl) * B,
where F, l, B are vector quantities.
Determining the direction of F is usually carried out in a very simple way - the rule of the left hand. Mentally, the left hand must be positioned so that the lines of magnetic induction (B) enter the open palm at an angle of 90 degrees, 4 straightened fingers indicate the direction of the current (from "+" to "-"), then the thumb bent at a right angle will indicate the direction of the current acting on the conductor with current Ampere force.
The best known force is the interaction of parallel currents. In fact, this is a special case of the general law. Imagine two parallel conductors with current in a vacuum, the length of which is infinite. The distance between them is denoted by the letter "r". Each conductor (currents I1 and I2) generates a magnetic field around itself, so they interact. The induction lines are circles.
The direction of the magnetic induction vector B1 is determined by the rule of the gimlet. We give the formula:
B1 = (m0 / 4Pi) * (2 * I1 / r);
where m0 is the magnetic constant; r is the distance; Pi - 3.14.
Applying the formula for finding the Ampere force, we get:
dF12 = (I2 * dl) * B1;
where dF12 is the force of the field of conductor 1 on conductor 2.
The modulus of force is:
dF12 = (m0 / 4Pi) * (2 * I1 * I2 / r) * dl.
If the length l is from zero to one, then:
F12 = (m0 / 4Pi) * (2 * I1 * I2 / r).
This is the force that acts on a certain unit of length of the wire with current. If you know the value of F, it becomes possible to design reliable electric machines, providing for the action of the Ampere force. It is also used to calculate the value of the magnetic constant. You need to pay attention that, based on the rule of the left hand, it follows: if the direction of the currents coincides, then the conductors are attracted, and otherwise repelled.