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Electromotive Force (EMF) in electromagnetism is defined as the amount of electricity passing through an electric source like a generator that gets converted into work done. This work done in the energy transformation (or conversion) is characteristic of any energy source that is capable of moving electric charges around the circuit. Electromotive force is measured in Volts or equivalent to 1 Coulomb of electric charge, and it is denoted by the symbol ε (or E).
EMF gets generated when magnetic fluctuations are caused over a surface. In the case of electrical generators, electromagnetic induction causes an electric field inside the generator. Potential differences are created between the generator terminals. Movement of electrons from one terminal to another causes a charge separation in the circuit. This causes a counter action from the electric voltage. Attaching a load thus helps drive the electric current through the circuit.
Read More: Current Electricity
Key Terms: Electromotive Force, EMF, Electric Circuit, Potential Difference, Terminal Voltage, Electric Charge, Electric Current, Circuit, Cell, Force
What is Electromotive Force?
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Electromotive force or EMF is the maximum potential difference between two electrodes of the cell with no current being drawn from the cell. The charges move in the electric circuit and we need to apply an external force to a given electric circuit for the motion of the charges in that given electric circuit.
The source for an external force can be a battery or any other potential difference-creating device. The external electric source applies a force that gives acceleration to the charges and it is known as the electromotive force.
Electromotive Force
The video below explains this:
Electromotive Force Detailed Video Explanation:
Important Observations From Above Diagram
- The battery is shown as a two-terminal device that keeps one terminal at a better potential than the other terminal.
- The upper potential is the positive terminal and it's generally labeled with a + sign.
- The lower-potential terminal is the negative terminal and is labeled with a - sign, this is considered as the source of the EMF.
- As you disconnect the source of the voltage from the lamp, the net flow of charges within the emf source becomes zero.
- On reconnecting the battery, charges travel again through one terminal of the battery on to the lamp.
- This causes lamp to glow and then the charges travel back to the battery’s opposite terminal.
- When considering the conventional positive current flow, the positive charges leave the positive terminal first and then travel through the lamp and enter the negative terminal of the battery (an EMF source).
- An EMF source is usually configured by this method.
Symbol for Electromotive Force
The symbol for EMF is E or sometimes it is ε.
Can Electromotive Force be Negative?
Yes, it is true that the (EMF) electromotive force can be negative. Let’s take an example where EMF is being generated by an inductor in such a way that it is opposing the incoming power. Then the EMF which is produced is considered negative as the direction of flow is opposite to the real power. Therefore, The statement of electronegative force being negative is true.
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Electromotive Force Formula
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Considering the formula for electromotive force as,
ε = V + Ir
Where
- The voltage of the cell is V.
- Current across the circuit is I.
- The internal resistance of the cell is R.
- The electromotive force is ε.
Read More: Difference between Emf and Voltage
Units of Electromotive Force
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- The electromotive force’s unit is in volts.
- The electromotive force (EMF) is said to be the total number of Joules of energy supplied by the source which is divided by each Coulomb to enable a unit electric charge to move across the circuit. It is Mathematically given by:
EMF = Joules Coulombs ⇒ ε = Joules Coulombs
Also Read: Current Electricity Important QuestionsDimensions of the Electromotive Force
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EMF is expressed as the ratio of the work done on a unit charge, and it is represented as:
EMF = Joules Coulombs
So, the dimension of EMF is M1L2T3I-1.
Derivation
Electromotive Force, EMF (ε) = Work Done(w.d) × [Charge]-1. . . . (1)
We know that, Work Done = Force × displacement
= Mass × acceleration × displacement = [M] × [M0 L1 T-2] × [L]
So, the dimensional formula of work done = M1 L2 T-2 . . . . (2)
And, Charge = current × time
∴ The dimensional formula of charge = I1 T1 . . . . (3)
On substituting equation (2) and (3) in equation (1) we get,
Electromotive Force = Work Done × [Charge]-1
Or, ε = [M1 L2 T-2] × [I1 T1]-1 = [M1 L2 T-3 I-1].
Therefore, dimensional formula of Electromotive Force or EMF is [M1 L2 T-3 I-1].
Read More: NCERT Solutions for Class 12 Current Electricity
Difference between Electromotive Force and Potential Difference
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The difference between Electromotive Force and Potential Difference is tabulated below:
| Electromotive Force | Potential Difference |
|---|---|
| It is defined as the work done on a unit charge. | It is defined as the energy which is dissipated as the unit charge pass through the components |
| It remains constant | Potential difference is not constant |
| It is independent of circuit resistance | It depends on the resistance between the two points during the measurement |
| Electric, magnetic, and the gravitational field are caused by EMF. | The only electric field is induced by Potential Difference. |
| It is represented by E or ε | It is represented by V. |
Difference between Electromotive Force and Terminal Voltage
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The difference between EMF and Terminal Voltage is listed below:
| EMF | Terminal Voltage |
|---|---|
| It is defined as the maximum potential difference that is delivered by the battery when there is no flow of current. | Terminal voltage is defined as the potential difference across the terminals of a load when the circuit is on. |
| It is measured by a potentiometer. | It is measured by a voltmeter. |
Discover about the Chapter video:
Current Electricity Detailed Video Explanation:
Notes on Electromagnetic Induction
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Given below are some important note son electromagnetic induction.
Things to Remember
- Electromotive force is the maximum potential difference between two electrodes of the cell with no current being drawn from the cell.
- The formula for electromotive force as ε = V + Ir.
- The electromotive force’s unit is in volts.
- EMF is mathematically expressed as the ratio of the work done on a unit charge.
- It is Mathematically given by EMF = Joules Coulombs ⇒ ε = Joules Coulombs.
- The dimension of EMF turns out to be M1L2T3I-1.
- Potential difference is the energy which is dissipated as the unit charge pass through the components.
- Terminal voltage is the potential difference across the terminals of a load when the circuit is on.
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Previous Year Questions
- in a metal under normal conditions is of the order of…. [NEET 1991]
- The current in the following circuit is...[NEET 1997]
- Kirchhoff's first law deals with….[NEET 1997]
- Identify the portion corresponding to negative resistance...[NEET 1997]
- bulb is connected to a 160 volts supply...[NEET 1997]
- The resistance between any two vertices of the triangle is...[JEE Main 2019]
- A uniform wire of length l and radius r has a resistance of….
- In a potentiometer experiment, when three cells A,B, and C are connected in series…..[KEAM]
- When two resistances R1 and R2 are connected in series, they consume 12W power….[KEAM]
- Nichrome is used as electrical heating element because of its…[KEAM]
- In the figure shown below, the terminal voltage across E2 is…[KEAM]
- In a potentiometer of wire length ll, a cell of emf V is balanced at a...[KEAM]
- The electrical permittivity and magnetic permeability of free space are… [ DUET 2003 ]
- Just after key K is pressed to complete the circuit, the reading will be …. [ KEAM 1999 ]
- The resistance between any two terminals is when connected in a triangle is…. [ NEET 1993 ]
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Sample Questions
Ques. What is the Measure of Electromotive Force? (1 mark)
Ans: It is measured in volts and is denoted by V.
Ques. Why is a potential difference always less than an electromotive force? (2 mark)
Ans: When a cell is charged, its positive electrode is connected to the positive terminal of the battery charger and the negative to the negative one. In this process, current flows from the positive electrode to the negative electrode inside the cell and the potential difference becomes greater than the cell emf.
Ques. Why is electromotive force scalar? (1 mark)
Ans: It is scalar because it is actually a potential difference and with units of volts. It is not actually a force but the voltage produced by a source of electrical energy like a battery. It is the amount of energy per unit charge and because Energy is a scalar, therefore EMF is also a scalar.
Ques. What is counter-electromotive force? (1 mark)
Ans: When a conductor is moved through a magnetic field, currents are generated inside the conductor and a second magnetic field is generated by those currents. The second field is opposite of the first field. This force is a Counter - Electromotive force.
Ques. How does the temperature affect the electromotive force? (1 mark)
Ans: As temperature rises the resistance wire increases and according to ohm’s law, the resistance is directly proportional to the electromotive force in volts.
So, when the temperature increases the resistance does too and hence the EMF increases.
Ques. State the difference between potential difference and electromotive force. (5 marks)
Ans. The differences are:
| Electromotive Force | Potential Difference |
|---|---|
| Electromotive force is the work done on a unit charge. | Potential Difference is the energy which is dissipated as the unit charge pass through the components |
| It remains constant | It is variable |
| Electromotive force is not dependent on circuit resistance | Potential Difference depends on the resistance between the two points during the measurement |
| Electric, magnetic, and the gravitational field are caused by EMF. | The only electric field is induced by Potential Difference. |
| It is represented by E or ε | It is represented by V. |
Ques. Can EMF be negative? (1 mark)
Ans. EMF or electromotive force can be negative. EMF is generated by an inductor in such a way that it opposes the incoming power. The EMF which is produced is considered negative as the direction of flow is opposite to the real power. Therefore, The statement of electronegative force being negative is true.
Ques. Define Electromotive force. (3 marks)
Ans. The motion of a magnet produces an induced potential difference with respect to the coil. This induced potential difference is known as electromotive force which sets up an induced electric current in the circuit. The motion of a magnet, with respect to the coil, produces an induced potential difference.
Ques. What are the units of EMF? (2 marks)
Ans. Eelectromotive force is abbreviated E in the international metric system but also, popularly, as emf. Despite its name, electromotive force is not actually a force, it is commonly measured in units of volts, equivalent in the metre–kilogram–second system to one joule per coulomb of electric charge.
Ques. Is emf voltage or current? (2 marks)
Ans. Emf is the voltage that is developed between two terminals of a battery or source, in the absence of electric current. Voltage is defined as the potential difference developed between the two electrode potentials of a battery under any conditions.
Ques. What is emf in open circuit? (2 marks)
Ans. The open-circuit voltage is also considered as the electromotive force (emf), which is the maximum potential difference when there is no current and the circuit is not closed. The opposite of an open circuit is a "short circuit".
Ques. A coil having n turns and area A is initially placed with its plane normal to the magnetic field B. It is then rotated through 180º in 0.2 sec. Find the emf induced at the ends of the coils. (2 Marks)
Ans. Total change in flux = ΔΦ = 2 nAB
Total time of change = Δt = 0.2s
Therefore, Emf induced = ΔΦ/Δt = 10nAB
Ques. A straight line conductor of length 0. 4m is moved with a speed of 7ms-1 perpendicular to a magnetic field of the intensity of 0.9wbm-2 Find the induced emf across the conductor. (2 Marks)
Ans. The induced emf across the conductor E= Blv
= 0.98 × 0.4 × 7 = 2.52V
Ques. Two conducting rings of radii r and 2r move in opposite directions with velocities 2v and v respectively on a conducting surface S. There is a uniform magnetic field of magnitude B perpendicular to the plane of the rings. Calculate the potential difference between the highest points of the two rings. (2 Marks)
Ans. Replace the emf in the rings with the cells.
E1= B2r(2V) = 4Brv
E2 = B(4r)v = 4Brv
V2 – V1 = 8Brv
Ques. A metal wheel with 20 metallic spokes each 1m long, is rotated with a speed of 180 rpm, in a plane perpendicular to the earth's field. at that place. If the magnitude of the field is 0.40 gauss, then calculate the emf between the axle and rim of the wheel. (5 Marks)
Ans. Solution is as follows:
- Motional emf: The emf induced due to motion relative to a magnetic field is called the motional emf.
- Consider a straight conductor PQ moving perpendicular to a uniform magnetic field B.
- Assume the motion of the rod to be uniform with a constant velocity of (v m/s).
- The rectangle PQRS forms a closed circuit enclosing a changing area due to the motion of the rod PQ.
- The magnetic flux ϕ enclosed by the loop PQRS can be given as: ⇒ ϕ = B × area = B × (l.x)
- Since the conductor is moving, there is a change in the rate of area moving. This causes a rate of change of flux which induces an emf.
- This induced emf is given by: \(⇒ \epsilon =\frac{-dϕ }{dt}=\frac{-d}{dt}(Blx) =-Bl\frac{dx}{dt}=Blv\)
Where \(-\frac{\mathrm{d} x}{\mathrm{d} t}=v\) is the speed of the conductor PQ
CALCULATION:
Given: number of spokes, n = 20 length of spokes, l = radius (r) = 1m, magnetic field (B) = 0.4 gauss = 0.4 × 10-4 tesla, and frequency (f) = 180 rpm = 3 rps
- The relation linear velocity and angular velocity is given by,
⇒ v = rω
Where ω is the angular velocity
Linear velocity of spoke at the axle = 0, and linear velocity at the rim end = rω .
- So the average liner velocity
\(⇒ v = \frac{0+rω }{2}= \frac{rω }{2}\)
- Angular velocity (ω) of the spoke is given as
⇒ ω = 2πf = 2π × 3 = 6π
- The emf between the axle and rim of the wheel.
⇒ ε = Blv = 0.4 × 10-4 × 1 × 0.5 × 6π = 3.77× 10-4 V
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