Foundation of Electromagnetism

Ampere’s Force Law was discovered by Andre-Marie Ampere (who formed the basis for the definition of the unit of electricity, Ampere). Without getting into tedious mathematical equations, we are going to understand what the law is, how Ampere was defined, and how this path-breaking law changed physics at that time.

Ampere’s Force Law

Ampere’s Force Law states that the force of attraction or repulsion between two wires carrying currents is proportional to their lengths and the intensities of current passing through them. If the currents flow in the same direction, repulsion takes place. If currents are flowing in opposite directions, the attraction takes place. The law is based on these two basic concepts of electrostatics:

• Biot-Savart Law states that every current-carrying wire produces a magnetic field around it, as shown in Figure 1.
• Lorentz force refers to the force that every magnetic field exerts on any electric charge moving in its field.

Figure 1: Thumb Rule to Find Magnetic Field Around a Current-Carrying Wire

Foundation of Electromagnetism

Based on the Biot-Savart Law and Lorentz force, there is a relationship between the magnetic field and electric charge/current. It is this relationship that Ampere sought to establish through experiments. The most basic of these experiments was to study the force between two current-carrying wires, as shown in Figure 2. This experiment and subsequent theories to explain its results laid the foundation of electromagnetism as a field in physics by itself.

Figure 2: Magnetic Field Between Current-Carrying Wires

Ampere, the SI unit of electric current, is defined as the electromagnetic force per unit length between two wires of infinite length, having the negligible diameter and placed 1 m apart in a vacuum. The basic assumption here is that the wires are in free space, i.e. there is no matter present that can be magnetized. If any matter present in the environment gets magnetized, it will exert its own magnetic force that will have to be taken into account, so this assumption has to be made.

Applications of Force Law

Using Ampere’s Force Law, the magnetic field around an infinite wire, infinite sheet, toroid, solenoid, or any other regular shape can be calculated, as shown in Figures 3 and 4 below.

Figure 3: Magnetic Field Around a Solenoid             

Figure 4: Magnetic Field Around a  Toroid

Ampere’s Force Law proved to be such a fundamental law that after him, many physicists like James Clerk Maxwell, Wilhelm Weber, Bernard Riemann, etc. extended it further to find a basic definition of force itself. Coming back to Ampere’s work, Force Law states that force between the current-carrying wires is proportional to their length and intensity of current flowing. This means that higher the current, greater is the attraction or repulsion between the wires.