EMF Formula

Electromotive force is one of the important concepts that help us understand the process of electromagnetism. The electromotive force is abbreviated as the EMF and it is closely associated with the more common concept of voltage. The electromotive force is the total energy provided by a battery or a cell per coulomb q of charge crossing through it.

The magnitude of EMF is equal to the potential difference across the cell terminals when there is no current flowing through the given electrical circuit and the formula used is known as the EMF formula. In this article, we will learn in detail the electromotive force formula, the idea of EMF physics and by the end with the help of the EMF equation with a few solved examples.

EMF Physics

The electromotive force can be defined as the total voltage or the potential difference across the terminals of the battery in an open circuit or in other words when no current is flowing through it. This might not appear like this as it would make a variance, but every battery will be built with some particular internal resistance. It is related to the regular resistance that reduces the flow of current in an electrical circuit, but it is enclosed only within the battery itself.

We know that when the circuit is open, no current will be flowing through the cell, this implies that the internal resistance of the battery will not change anything because there is no current for it to reduce or slow down. Thus, the electromotive force can be considered as the maximum potential difference or the voltage across the two terminals in an idealized condition. This explains the EMF physics and we can understand from this that the electromotive force is a special case of the voltage difference.

Now, the question that arose was even though the electromotive force is not a form of force at all, then why is it referred to as the electromotive force, what is the difference between the EMF and regular potential difference, and what will be the source of EMF? 

To answer these doubts, consider a simple electrical circuit of a lamp connected to a battery.

We know that any electro voltaic device can be expressed as a two-terminal device that keeps one terminal at a higher potential and another terminal at a lower potential. The higher electric potential is commonly known as the positive terminal and it is generally designated with a plus sign. The lower-potential terminal is known as the negative terminal and is designated with a minus sign. This is called the source of the EMF.

When the source of the electromotive force is disconnected from the lamp i.e., when the circuit is open, then there is no net movement of charges within the given EMF source. Once the circuit is closed then or reconnected to the lamp, charges will move from one terminal of the battery, through the lamp and this further will result in the lamp glowing and back to the other terminal of the battery. 

If we consider the conventional flow of electric current i.e., positive current, positive charges tend to leave the positive terminal, drive through the lamp, and enter the negative end of the EMF source. This is how an EMF source is arranged. At the same time, the electromotive force of a battery is the potential difference developed at both ends of the given battery.

Therefore, EMF physics explains that the electromotive force is the total energy supplied by a battery or a cell per coulomb of charge passing through it. The total magnitude of EMF is equal to the voltage or the potential difference across the terminals of the battery when there is no current moving through the given electrical circuit.

EMF Equation

We know that the charges circulate in the electric circuit, for the motion of the charges in a given electric circuit we need to apply an external force to it. We say that an external electric source such as a battery uses such force which will give acceleration to the charges and it is kenned as the electromotive force. Despite its name, it's not a form of force but a potential difference it is a special case of potential difference and it is generally denoted by the symbol.

Now, let us have a look at the EMF equation:

According to the definition of EMF and EMF physics, the EMF formula is given by:

\[\Rightarrow\] EMF = \[\varepsilon\] = \[\frac{E}{Q}\] ....(1)

Where,

E - The total energy of the battery

Q - The total charge flowing through the given circuit

Equation (1) can be used if we know the total energy of the battery used in the circuit. The electromotive force is also the potential difference developed in the circuit, thus, the EMF formula can also be found using the ohm’s law. Hence we write:

ε = IR…..(2)

Where,

I - The total current flowing in the circuit

R - The total resistance used in the circuit

Since we know that the EMF depends upon the internal resistance of the battery, we should replace the resistance with the sum of the resistance and the internal resistance. Thus equation (2) becomes:

ε = I (r + R)

ε = Ir + IR

ε = V + Ir…….(3)

Where,

V - The total potential difference developed in the circuit

I - The total current flowing in the circuit

r - The internal resistance of the battery

Therefore, equation (1) and equation (3) are known as the EMF formula or the EMF equation. Let us understand the EMF formula and how to find EMF or how to calculate EMF with a few solved examples.

Examples:

1. Consider an electrical circuit with a potential difference of 5V, with a current of1 A. If the internal resistance of the battery used is 0.8 ohms. Then, determine the EMF of the circuit using the EMF formula.

Ans:  Given,

The potential difference of the electric circuit = V = 5 volts

The total current flowing through the circuit = I = 1 A

The internal resistance of the battery = r = 0.8 ohms

We are asked to determine the EMF of the circuit using the EMF equation. We know that the EMF of the circuit can be calculated using the formula given below:

ε = V + Ir…….(1)

Where,

V - The total potential difference developed in the circuit

I - The total current flowing in the circuit

r - The internal resistance of the battery

Substituting the value of potential difference, current and the internal resistance in equation (1) we get:

ε = V + Ir

ε = 5 + (10.8)

ε = 5.8 volts

Therefore, the EMF of the circuit using the EMF formula is 5.8 Volts.

2. Calculate the terminal potential difference of a battery when it is connected to a 10-ohm load with battery EMF, ε = 3 volts and the internal resistance of the battery is 2 ohm.

Ans:  Given, The total EMF of the battery = ε = 3 volts

The external load applied to the battery = RL = 10 ohms

The internal resistance of the battery = r = 2 ohms

Now, we are asked to determine the terminal potential difference of the battery. Before that let us calculate the current flowing through the given circuit. according to ohm’s law, we know that:

\[\Rightarrow\] I = \[\frac{V}{R}\] = \[\frac{\varepsilon }{r+R_{L}}\] ….(1)

I = 3/12 = 0.25 amp

Now, let us determine the terminal potential difference of the battery. The EMF formula is given by:

ε = V + Ir…….(2)

Where,

V - The total potential difference developed in the circuit

I - The total current flowing in the circuit

r - The internal resistance of the battery

Substituting the value of EMF, current and the internal resistance in equation (2) we get:

3 = V + (0.252)

V =3 - 0.5

V = 2.5 Volts

Therefore, the terminal potential difference of the battery is 2.5 volts.

Distinctions between Terminal Voltage and EMF:

When the circuit is turned on, the terminal voltage is defined as the potential difference across the terminals of a load. While EMF is defined as the highest potential difference delivered by the battery when no current flows.

The EMF may be expressed in terms of the battery's internal resistance (r), where: I(r+R) = I(r+R)

We may then reorganise this in terms of terminal resistance using Ohm's law: = V+Ir+V+V+V+V+V+V+V+V

For varying resistances, the EMF of the cell may be calculated by measuring the voltage across the cell with a voltmeter and the current in the circuit with an ammeter.

According to Faraday's law, every change in a coil's magnetic field will cause an EMF to be generated in the coil (and hence also a current).  

Using Faraday's rule, society has profited from vital technologies like transformers used in the transmission of power in the UK national grid, which is now a requirement of our houses. It is also utilised in electric generators and motors, such as hydroelectric dams, to generate power, which is now essential to our contemporary technological demands. MAG-DRIVE, a current Birmingham research project, is looking for ways to create and enhance permanent magnet materials that can be utilised in the future generation of electric cars. Because EMF is created by solar cells, it is essential in renewable energy research areas.

EMFs are Often classified into One of two Types based on Their Frequency:

• Non-ionizing: low-level radiation that is widely regarded as safe for humans.

• Ionising radiation is high-level radiation that has the potential to cause cellular and DNA damage.

Currently, scientific data does not decisively link mobile phone usage to any detrimental human health consequences, while scientists acknowledge that additional study is required.

Non-ionizing EMFs can be found in both natural and man-made environments. The magnetic field of the Earth is an example of a natural EMF. 

EMFs at extremely low frequencies (ELF-EMFs). Power lines, electrical cabling, and personal equipment such as electric shavers, hairdryers, and electric blankets may all produce this non-ionizing radiation field.

Radiation of radiofrequency frequency. Wireless gadgets such as mobile phones, smart metres, tablets, and laptop computers create this non-ionizing radiation field. Radio and television broadcasts, radar, satellite stations, and MRI equipment all produce it.

A Quick Review:

The electromotive force is defined as the voltage at the source's terminals in the absence of an electric current. The phrase electromotive force refers to the amount of effort necessary to separate the charge carriers in the source current so that the force acting on the source terminals' charges is not the field's direct result. What exactly is electromotive force? The electromotive force (EMF) is defined as the product of the amount of work done in the energy transformation (or conversion) and the quantity of electricity that goes through the electrical source or generator. The electromotive force (EMF) is measured in Volts and is represented by the symbol (or E). In this post, we will mostly cover what is electromotive force, what is emf in physics, and so on.

The electric potential created by an electrochemical cell or by altering the magnetic field is referred to as electromotive force. We know that charges move in an electric circuit; but, for the charges to move in a specific electric circuit, we must apply an external force to it. Despite its name, EMF is not exactly a force but a potential difference.

The transfer of energy from one form to another is accomplished through the use of a generator or a battery. One terminal in these devices becomes positively charged, while the other becomes negatively charged. As a result, an electromotive force is defined as work done on a unit electric charge.

The electromagnetic flowmeter, which is an application of Faraday's law, employs electromotive force.