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# Induced emf definition and formulas

Induced emf (electromotive force) is defined as the potential difference induced in a (coil or a) conductor by the changing magnetic flux linking to it. The magnitude of induced emf depends on several factors such as, number of turns in coil (if it is a coil), length of the conductor moving, relative velocity between conductor and magnetic flux, and magnetic flux strength.

When the conductor is a closed path a voltage or current is looped through a circuit. The direction of current and voltage is depend on several factors. We will explain them on upcoming sections in this articles one by one.

## What is emf (Electromotive force)?

Emf is, energy per unit electric charge that is imparted by an energy source, such as an electric generator or a battery. Energy is converted from one form to another in the generator or battery as the device does work on the electric charge being transferred within itself. One terminal of the device becomes positively charged, the other becomes negatively charged.

Similarly we can say the same in other words, that is the work done on a unit of electric charge, or the energy thereby gained per unit electric charge, is the emf. Electromotive force is the characteristic of any energy source capable of driving electric charge around a circuit. It’s denoted as emf in standard.

You can get a clear idea from above graphical representation.

Faraday’s law of induction  gives the mathematical approach to induced emf. The induced emf in a coil having N number of turns is given by rate of change of magnetic flux in given time.

## Factors affecting the Induced emf

There are several factors affecting magnitude of induced emf based on different arrangements.

When we consider a coil inside the magnetic field, following  are the factors affecting the magnitude of induced emf,

1. Number of turns in the coil (N) – By increasing the amount of individual conductors cutting through the magnetic field, the amount of induced emf produced will be the sum of all the individual loops of the coil.
Example: If there are 20 turns in the coil there will be 20 times more induced emf than in one piece of wire.
2. Relative motion between the coil and the magnet (v) – If the same coil of wire passed through the same magnetic field but its speed or velocity is increased, the wire will cut the lines of flux at a faster rate so more induced emf would be produced.
3. Magnetic field Strength (B) – If the same coil of wire is moved at the same speed through a stronger magnetic field, there will be more emf produced because there are more lines of force to cut.
When a conductor (rod) is moved inside the magnetic field then following factors will define the induced emf.
1. Length of the conductor (l): Effective length which is crossing magnetic flux lines is a factor that increases induced emf.
2. Angle between magnetic flux lines and conductor movement direction (θ): When the moving conductor is perpendicularly cross the magnetic flux lines, then the induced emf will be maximum compared to when the conductor crosses magnetic flux lines at an angle (θ). When the conductor moving in direction of magnetic flux lines, there is no crossing magnetic flux by the conductor and induce emf will be zero.
3. Magnetic Field Strength (B): If the same conductor is moved at different magnetic field strength (B) at the same speed and angle, there will be different emf produced because there are more lines of force to cut. Greater the magnetic field strength, more the induced emf.

## Types of Induced emf

So far we explained the factors affecting induced emf. By changing one or more of those factors we can change the induced emf. Induced emf can be categorized into two based on the emf induction process. With those combinations of changes, we can divide the induction process as,

1. Statically Induced emf
2. Dynamically Induced emf

### 1. Statically Induced emf

Statically induced emf is, as name itself explain what it is, the magnetic flux source and conductor/coil is kept static and magnetic flux strength (B) is changed. Their for induced emf change without any dynamic movements in the system.

### 2. Dynamically Induced emf

Dynamicall Induced emf also, as name explains, the coil/conductor keeps on moving to make the linking magnetic flux change. By this way induced emf changes.

### Demonstration of induced emf

Say we were able to move the magnet in the diagram on right, in and out of the coil at a constant speed and distance without stopping. Then we would generate a continuously induced voltage that would alternate between one positive polarity and negative polarity.

They will produce an alternating or AC output voltage. This is the basic principle of how an electrical generator works similar to those used in dynamos and car alternators.

We can conclude that, when we move the magnet inside the coil, the magnetic flux lines linking with coil induces the voltage, therefore we can observe a current passing through the galvanometer.

Another fact we should note from the example above is, the moving direction has an impact on the polarity of induced emf. When the magnet is moved inside the coil, the galvanometer indicator moves from center to a side (left or right), and when the magnet is taken out from the coil, galvanometer indicator moves opposite side. That is due to the rate of change in the linking flux. When flux linkage increasing, the current also increases and vise versa.

Further, keeping the magnet in zero velocity won’t induce any emf in the coil. So, we can observe the galvanometer indicator in center (zero) position.

### Generator – An application of induced emf

In small generators such as a bicycle dynamo, a small permanent magnet is rotated by the wheel of the bicycle inside a fixed coil. Alternatively, an electromagnet powered by a fixed DC voltage can be made to rotate inside a fixed coil, such as in large power generators producing in both cases an alternating current.

Suggested reading: Read our article on Electromagnetic induction, application and laws related to it.

Hope you have got a brief idea on what are the factors affecting the magnitude of induced emf. If you have any questions from this section please write to us.