96. Electromotive force, EMF

The electric field cannot provide a direct electric current in a closed circuit because the electrostatic field work along the closed circuit is zero. The passage of electric current along the circuit is accompanied by the emission of energy in the form of heat. Therefore, there must be some kind of power source in any circuit that supplies it to the circuit. Question is what forces are involved in this process.

It is obvious that in a closed circuit, along with the forces of the electrostatic field, some forces of a different non-electrostatic nature must act on moving charges. The work of these forces along a closed circuit must be different from zero. It is not necessary that these forces act in all parts of the conductor, but in some parts they are necessary.

To quantify the forces that result in an electric current being generated in a circuit, a special value, called external forces tension \(\,\overrightarrow{E}_{ext}\,\), is introduced.

The external force tension is a numerical value equal to the force acting on a single positive charge, which is due whatever reasons except the electrostatic field.

In a galvanic cell or battery it is a chemical force of a complex electromagnetic nature, in a power plant generator it is a magnetic force, and so on.

It is the work of external forces that ultimately determines the existence of electric current in a closed circuit. External forces drives the charges in the individual parts of the circuit, which further causes the formation of surface charges along the entire conductor and the electric field inside it. It is the work of external forces that generate heat as the electric current passes through.

The quantity, numerically equal to the work of external forces that move a single positive charge along the circuit, is called electromotive force \(\,\mathcal{E}\,\) (abbreviated - EMF).

\( \mathcal{E} \,= \,\frac{W_{ext}}{Q} \)

As can be seen from the definition, EMF is the work of moving a charge, not the force.

It is possible to speak of electromotive force in any part of a circuit. It is the work of external forces not in the entire circuit, but only in a given section. The EMF of a galvanic element is the work of external forces when moving a single positive charge inside an element from one pole to another.

Since EMF is a work, it is not a vector. The EMF sign can be either positive or negative.

The analogy between electric current and liquid flow.

To understand this better, let us look at the analogy between the electric current in a conductor and the liquid flow through pipes. In any section of a horizontal pipe, liquid flows because of the difference in pressure at the ends of the section. The liquid moves in the direction of pressure reduction. But the force of pressure in a liquid is a type of elastic force that is potential, like the Coulomb force. Therefore, the work of these forces on a closed path is equal to zero and these forces alone are not able to cause long circulation of the liquid through the pipes. Liquid flow is accompanied by energy loss due to friction forces. For water circulation, a pump is needed. The piston of the pump acts on a liquid and creates constant difference of pressure on an input and an output of the pump. Therefore the liquid flows through the pipe. A pump is an analogy of an electric current source, where the role of external forces is the force acting on water from the moving piston.