Electrical Principles
Chapter 12 Electromagnetic Induction
Chapter outline
An electric current produces a magnetic field, and as explained in this chapter, a moving magnetic field can cause an electric current. This is called electromagnetic induction and is how most electrical power is generated.
This chapter:
- introduces the inductor
- explains the property called inductance and some of its effects.
Contents
- 12.1 Introduction
- 12.2 Electromagnetic induction
- 12.3 Lenz’s law
- 12.4 Inductance
- 12.5 Mutual inductance
- 12.6 The LR circuit
12.1 Introduction
In 1820, Oersted discovered the link between electricity and magnetism. In 1831, Michael Faraday found that a moving magnetic field causes a current to flow in a conductor. Faraday’s law
This effect, called electromagnetic induction, was studied by many notable people of the time.
The first DC generator was produced in 1832, and today most electrical power is produced by electromagnetic induction
12.2 Electromagnetic induction
A conductor moving in a magnetic field causes a voltage to be induced in the conductor.
The polarity of the induced voltage changes with the direction of movement.
Fleming’s right-hand rule
Fleming’s right-hand rule gives a way of determining the direction of the induced current when a conductor is moving in a magnetic field.
Voltage induced in a conductor
The value of the voltage induced in a conductor is proportional to the:
- length of the conductor in the magnetic field
- speed of relative movement between the conductor and the magnetic field
- strength of the magnetic field.
It is also affected by the angle at which the conductor passes through the magnetic field. This is assumed to be a right angle (90º).
Calculating induced voltage (e)
e = Blv
Where:
- e = induced EMF in volts
- B = flux density of the magnetic field (teslas)
- l = length of the conductor moving at right angles to the field (metres)
- v = velocity of the conductor (metres per second).
Induced Voltage: Apply
Solve the following:
Given:
- Velocity (v) = 10 m/s
- Magnetic flux density (B) = 0.001 T
- Conductor length (l) = 0.01 m
Find: Induced voltage (e)
Inducing a voltage in a coil
Inducing a voltage in a coil
Winding the conductor into a coil increases its length, and therefore increases the induced voltage.
No motion, no induced voltage
A voltage is induced in a coil only when the magnet is moving
Reversing direction of motion
The polarity of the induced voltage reverses when the direction of motion is reversed.
Voltage Induced in a Coil
Faraday’s Law gives us another way to calculate induced voltage:
e = N × (rate of change of flux)
Where:
- e = induced EMF (volts)
- N = number of turns on the coil
-
rate of change of flux = how quickly magnetic flux
(in webers) is changing with respect to time
(flux cut per second)
This form of Faraday’s Law comes from considering how a changing magnetic field links with the coil. If flux through the coil changes, a voltage is induced. More turns (N) means the flux change is experienced multiple times, increasing the induced voltage.
Induced Voltage: Apply
Solve the following:
Given:
- Number of turns (N) = 500
- Flux change = 10 mWb (0.01 Wb)
- Time interval = 100 ms (0.1 s)
Find: Induced voltage (e)
Induced EMF: Apply
Solve the following:
Given:
- Number of turns (N) = 1500
- Flux change rate = 0.01 Wb every 5 seconds
Find: Induced EMF (e)
Induced EMF: Apply
Solve the following:
Given:
- Number of turns (N) = 800
- Flux change (ΔΦ) = 0.024 Wb
- Time interval (Δt) = 0.12 s
Find: Induced EMF (e)
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Inductance - 12.3 Lenz’s law
Lenz’s law states
the current induced in a conductor will set up a magnetic field that opposes the magnetic field causing the current. This opposition is called inductance.
Opposition to conductor motion
- Fleming’s right-hand rule gives the direction of the induced current.
- It shows the current is flowing towards you, causing an anticlockwise field around the conductor. The fields repel because their lines of force are in the same direction.
Lenz’s law acting in a coil
Lenz’s law – the coil’s magnetic field opposes the movement of the magnet
Lenz’s Law Check
Test your understanding of electromagnetic induction.
12.4 Inductance
Inductance is:
- the property of a circuit, component or conductor that opposes a change in the value of an electric current
- increased when a conductor is wound into a coil.
Back-EMF of a coil
A coil produces a back-EMF while the magnetic field builds up, because the expanding field is moving.
No motion, no back-EMF
When the field has built up, there is no relative motion and therefore no induced voltage.
The inductor
An inductor is a component that has a coil of wire wound around a core. Therefore, it has inductance.
Inductance is measured in henrys (H). A coil has an inductance of 1 H if a voltage of 1 V is induced in the coil when the current in the coil is changing by 1 A per second.
Inductor symbols:
Factors that determine inductance
The inductance of a coil is determined by:
- number of turns
- length of the coil
- cross-sectional area of the coil
- permeability of the core.
Lets break that down
Number of turns
Inductance is proportional the square of the number of turns. That is, double the turns gives four times the inductance.
Area of the coil
Inductance is directly proportional to the cross-sectional area of a coil.
Permeability of the core
Inductance is directly proportional to the permeability of the core.
Inductor cores
Three main types of core materials used with inductors are:
- Air (or other non-magnetic materials) – good for high frequency, harmonic applications and communications
- Soft iron – transformer cores and low frequency applications
- Ferrite – medium frequency applications, signal transformers
Equation for Inductance
\[ L = \frac{n^2 A \mu}{l} \]
Where:
- \( L \) = inductance in henrys
- \( n \) = number of turns
- \( A \) = cross-sectional area (m²)
- \( \mu \) = permeability of the core
- \( l \) = length of the coil (m)
Magnetic Flux and Induced EMF
Magnetic Flux \( (\Phi_B) \): The magnetic flux through a coil with \( N \) turns is:
\[ \Phi_B = N \cdot B \cdot A \]
where \( B \) is the magnetic field strength and \( A \) is the cross-sectional area of the coil.
Induced EMF: According to Faraday’s Law:
\[ \text{EMF} = -N \frac{d\Phi_B}{dt} \]
Relating Flux to Current: The magnetic flux is proportional to the current:
\[ \Phi_B = L \cdot I \]
Combining Equations: Substitute \( \Phi_B = L I \) into the EMF equation:
\[ \text{EMF} = -N \frac{d(L I)}{dt} \]
Since inductance \( L \) is constant for a given coil:
\[ \text{EMF} = -L \frac{dI}{dt} \]
Induced EMF from Inductance: Apply
Solve the following:
Given:
- Inductance (L) = 0.5 H
- Rate of change of current (dI/dt) = 4 A/s
Find: Induced EMF
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Icons as e Anchors
Use Bootstrap’s grid for layout, and its flex utilities for alignment — no custom flex rules needed.
This keeps the CSS simpler and more maintainable.
Icons as e Anchors
Use Bootstrap’s grid for layout, and its flex utilities for alignment — no custom flex rules needed.
This keeps the CSS simpler and more maintainable.
Ohm's Law: Apply
Solve the following:
Given:
- Voltage (V) = 12 V
- Resistance (R) = 6 Ω
Find: Current (I)
Icons as Visual Anchors
Use Bootstrap’s grid for layout, and its flex utilities for alignment — no custom flex rules needed.
This keeps the CSS simpler and more maintainable.
Icons as Visual Anchors
Use Bootstrap’s grid for layout, and its flex utilities for alignment — no custom flex rules needed.
This keeps the CSS simpler and more maintainable.
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