Electromotive Force

Electromotive force refers to the electric potential whose production takes place by either electrochemical cell or by facilitating a change in the magnetic field. The use of a battery or generator takes place for converting energy from one form to another form. The electromotive force symbol that has been accepted by experts is ε.

Introduction of Electromotive Force

Electromotive force refers to the electrical action whose production takes place by a non-electrical source. Furthermore, transducers refer to devices that provide an emf by facilitating conversions of other forms of energy into electrical energy, like generators or batteries.  Moreover, batteries convert chemical energy while generators convert mechanical energy.

In electromagnetic induction, one can define electromotive force around a conductor’s closed-loop as the electromagnetic work that would take place on an electric charge if it travels once around the loop. For a time-varying magnetic flux which would link a loop, one cannot define the scalar field of an electric potential because of a circulating electric vector field.

electromotive force

Electromotive Force

How do we Measure Electromotive Force?

Electromotive force is the energy per unit electric charge which an energy source imparts. Furthermore, this energy source can be a battery or an electric generator. Moreover, the conversion of energy from one form to another in the battery or generator happens as the device works on the charge whose transference is taking place within.

One terminal of the device becomes negatively charged while the other would become positively charged. Furthermore, electromotive force is the work that takes place on a unit of electric charge. Moreover, this force refers to the characteristic of any energy source that can drive the electric charge around a circuit.

Despite its name, this force cannot be termed as a force. Its measurement commonly takes place in units of volts. This is equivalent in the metre–kilogram–second system to one joule per coulomb of electric charge. Moreover, when it comes to the electrostatic units of the centimetre–gram–second system, the statvolt, or one erg per electrostatic unit of charge happens to be the unit of electromotive force.

Formula of Electromotive Force

The exertion of the magnetic force on the charges in a moving conductor will lead to a generation of a motion whose association can take place with a voltage. Furthermore, the voltage that is generated can be seen to be the work done per unit charge.

Furthermore, motional EMF = velocity of the charge carriers *magnetic field * length of the wire

The electromotive force formula is:

EMF = v B L


EMF: Electromotive force

v: Velocity of the charge

B: Magnetic field

L: Length of the wire where the movement of the charge is happening

Derivation of the Formula of Electromotive Force

The formula for an electromotive force that is induced by a straight conductor moving in a magnetic field can be expressed by the following equation:

E = B * l * v

E = electromotive force

B = magnetic field

l = length of conductor

v = velocity of conductor

This equation comes from the Faraday-Lenz law which one can define it by the following:

E = -(N * ∆ɸ)/∆t

Because ɸ, or magnetic flux, is affected mainly due to the magnetic field B’s strength, or the area that is bounding the magnetic field A, ∆ɸ must be either ∆B*A or B*∆A. Furthermore, in the case of a moving straight conductor, there would be no change in the magnetic field, but the change would happen in the bounding area. Thus, in this equation,

∆ɸ = B * ∆A


E = -(N * B* ∆A)/∆t

Furthermore, because it is a straight conductor that is devoid of any coils, N is equal to 1. Thus, the equation becomes:

E = -(B * ∆A)/∆t

Now, when it is known that it involves a straight conductor, the change in the bounding area that is due to the motion will be rectangular. Therefore, one can define the area by l * w, where l is the area’s length and w is the area’s width. As such, a change in the area must be due to a change in either l or w, so ∆A = l * ∆w. The equation becomes:

E = -(B * l * ∆w)/∆t

One can define velocity as the change that takes place in distance divided by a change that takes place in time. Also, since the width is certainly a measurement of distance, ∆w/∆t would turn out to be equal to velocity. The equation becomes:

E = -B * l * v

Finally, the equation would lose the negative sign because voltage happens to be a scalar measurement and lacks a direction. This results in the formula

E = B * l * v

FAQs on Electromotive Force

Question 1: What is the difference between the electromotive force and terminal voltage?

Answer 1: One can define terminal voltage as the potential difference across a load’s terminals when the circuit is on. In contrast, an electromotive force is the maximum potential difference that a battery can deliver when there is no flow of current.

Question 2: What is the difference between the electromotive force and potential difference?

Answer 2: Both the potential difference and electromotive force happen to be a form of energy. One of the main differences that exist between the electromotive force and potential difference is that the former happens due to the conversion of the other form of energy into electrical energy whereas in potential difference the conversion of electrical energy takes place into other forms of energy.

Question 3: Is it possible for the electromotive force to be negative?

Answer 3: Yes, it is certainly possible for this force to be negative. Consider an example where the generation of this force is taking place by an inductor such that it is opposing the incoming power. In such a case, the produced electromotive force would be negative as the flow’s direction is opposite to the real power.

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