SSS 3: ELECTROMAGNETIC INDUCTION
Electromagnetic induction is the phenomenon in which an electromotive force (e.m.f.) is induced in a conductor whenever there is a change in the magnetic flux linking the conductor.
If the conductor forms a closed circuit, the induced e.m.f. produces an induced current.
2. Faraday's Experiment
Michael Faraday discovered electromagnetic induction through experiments involving a coil, a galvanometer and a bar magnet.
When a bar magnet is moved towards a coil, the galvanometer shows a deflection, indicating that current is produced.
When the magnet is held stationary inside or near the coil, there is no deflection.
When the magnet is moved away from the coil, the galvanometer deflects in the opposite direction.
Conclusion
An e.m.f. is induced only when there is a change in magnetic flux through the coil.
3. Magnetic Flux
Magnetic flux is the total number of magnetic field lines passing normally through a given surface.
It is represented by Φ (phi).
The formula is:
Φ = BA cos θ
Where:
Φ = magnetic flux (Wb)
B = magnetic flux density (T)
A = area of the coil (m²)
θ = angle between the magnetic field and the normal to the surface
The SI unit of magnetic flux is the weber (Wb).
Faraday's Laws of Electromagnetic Induction
First Law
Whenever there is a change in the magnetic flux linking a conductor, an e.m.f. is induced in the conductor.
If the circuit is closed, an induced current flows.
Second Law
The magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage.
For a coil of N turns:
E = -N ΔΦ/Δt
Where:
E = induced e.m.f. (V)
N = number of turns
ΔΦ = change in magnetic flux (Wb)
Δt = time taken for the change (s)
The negative sign indicates Lenz's law.
For magnitude only:
E = N ΔΦ/Δt
Lenz's Law
Lenz's law states that the direction of an induced current is such that its magnetic effect opposes the change in magnetic flux that produces it.
In simple terms:
The induced current always opposes the change causing it.
For example, when a north pole of a magnet is moved towards a coil, the near face of the coil becomes a north pole to oppose the approaching magnet.
Factors Affecting the Magnitude of Induced E.M.F.
The induced e.m.f. can be increased by:
Increasing the number of turns of the coil.
Increasing the strength of the magnetic field.
Moving the magnet or coil faster.
Increasing the area of the coil.
Increasing the rate of change of magnetic flux.
Ways of Producing Electromagnetic Induction
Electromagnetic induction can be produced by:
1. Moving a magnet into or out of a coil.
2. Moving a coil through a magnetic field.
3. Rotating a coil in a magnetic field.
4. Changing the strength of the magnetic field around a stationary coil.
5. Changing the area or orientation of a coil within a magnetic field.
Direction of Induced Current
The direction of induced current can be determined using:
Fleming's Right-Hand Rule
Stretch the thumb, first finger and second finger of the right hand so that they are mutually perpendicular.
Thumb → direction of motion of the conductor
First finger → direction of magnetic field
Second finger → direction of induced current.
Motional E.M.F.
When a conductor of length l moves with velocity v perpendicular to a magnetic field of flux density B, an e.m.f. is induced.
The formula is:
E = Blv
Where:
E = induced e.m.f. (V)
B = magnetic flux density (T)
l = length of conductor (m)
v = velocity of conductor (m s⁻¹)
If the conductor moves at an angle θ to the magnetic field:
E = Blv sin θ
Applications of Electromagnetic Induction
Electromagnetic induction is used in:
(a) Electric Generators
Generators convert mechanical energy into electrical energy using electromagnetic induction.
(b) Transformers
Transformers use electromagnetic induction to increase or decrease alternating voltage.
(c) Induction Cookers
A changing magnetic field induces currents in the cooking vessel, producing heat.
(d) Microphones
Some microphones use electromagnetic induction to convert sound vibrations into electrical signals.
(e) Bicycle Dynamos
A dynamo uses electromagnetic induction to generate electrical energy for bicycle lamps.
11. Electromagnetic Induction in a Generator
An AC generator consists mainly of:
Armature/coil
Strong magnetic field
Slip rings
Carbon brushes
Shaft
When the coil rotates in the magnetic field, the magnetic flux linking the coil continuously changes. An e.m.f. is therefore induced.
The direction of the induced current changes every half rotation, producing alternating current (AC).
Difference Between Electromagnetic Induction and Electrostatic Induction
Electromagnetic Induction
Electrostatic Induction
Caused by changing magnetic flux
Caused by the presence of a charged body
Produces induced e.m.f.
Produces separation of charges
Involves magnetic fields
Involves electric fields
Used in generators and transformers
Used in electrostatic devices
Example
A coil of 200 turns experiences a change in magnetic flux from 0.02 Wb to 0.08 Wb in 0.5 s. Calculate the induced e.m.f.
Solution
Given:
N = 200
Initial flux = 0.02 Wb
Final flux = 0.08 Wb
Δt = 0.5 s
Change in flux:
ΔΦ = 0.08 − 0.02
ΔΦ = 0.06 Wb
Using:
E = N ΔΦ/Δt
E = (200 × 0.06) / 0.5
E = 24 V
Therefore:
Induced e.m.f. = 24 V
Key Points to Remember
No change in magnetic flux → no induced e.m.f.
Greater rate of change of flux → greater induced e.m.f.
More turns → greater induced e.m.f.
Lenz's law determines the direction of induced current.
Faraday's law determines the magnitude of induced e.m.f.
Generators operate mainly on electromagnetic induction.
Transformers operate through electromagnetic induction.
MAGNETIC FIELD OF A SOLENOID
A solenoid is a long cylindrical coil consisting of many turns of insulated wire wound closely together.
When electric current flows through the solenoid, it produces a magnetic field.
The magnetic field is produced around and inside the solenoid.
A solenoid behaves like a bar magnet, having a north pole (N) and a south pole (S).
APPLICATIONS OF ELECTROMAGNETIC FIELDS
Electromagnetic fields have many applications in everyday life and technology.
1. Loudspeaker
A loudspeaker uses the interaction between a permanent magnetic field and a current-carrying coil to produce vibrations that generate sound.
2. Electric Generator
It operates on the principle of electromagnetic induction.
3. Transformer
A transformer uses electromagnetic induction to transfer electrical energy between two circuits. It can increase or decrease alternating voltage.
4. Electric Motor
An electric motor converts:
\[
\boxed{\text{Electrical energy}\rightarrow\text{Mechanical energy}}
\]
5. Moving-Coil Galvanometer
A moving-coil galvanometer uses the torque produced when a current-carrying coil is placed in a magnetic field to detect and measure small electric currents.
---
7. ELECTRIC MOTOR
An electric motor is a device that converts electrical energy into mechanical energy.
Principle of an Electric Motor
An electric motor works on the principle that:
> A current-carrying conductor placed in a magnetic field experiences a force.
When a current-carrying coil is placed between the poles of a magnet, forces act on opposite sides of the coil. These forces form a couple and produce a turning effect or torque, causing the coil to rotate.
Main Parts of a Simple DC Motor
1. Permanent magnet
2. Armature or coil
3. Split-ring commutator
4. Carbon brushes
5. Axle
6. Battery or DC power supply
Functions of the Main Parts
Permanent Magnet
Provides the magnetic field.
Armature
The coil through which current flows and which rotates.
Split-Ring Commutator
Reverses the direction of current in the coil after every half-turn, thereby maintaining continuous rotation.
Carbon Brushes
Provide electrical contact between the external circuit and the rotating commutator.
Axle
Supports the coil and transfers the rotational motion.
Working of an Electric Motor
1. Current flows through the coil.
2. The coil lies within a magnetic field.
3. Magnetic forces act on opposite sides of the coil.
4. The forces form a couple.
5. The couple produces torque.
6. The coil rotates.
7. The split-ring commutator reverses the current every half-turn.
8. Continuous rotation is maintained.
Diagram: Electric Motor
Draw and label:
N and S poles
Armature/coil
Split-ring commutator
Carbon brushes
Battery
Axle
Direction of rotation.
---
8. MOVING-COIL GALVANOMETER
A moving-coil galvanometer is a sensitive instrument used to detect and measure small electric currents.
Principle
It operates on the principle that:
> A current-carrying coil placed in a magnetic field experiences a torque.
The torque causes the coil and attached pointer to rotate.
For a simple galvanometer:
\[
\boxed{\tau=N B I A}
\]
Where:
\(\tau\) = magnetic torque (N m)
\(N\) = number of turns of the coil
\(B\) = magnetic flux density (T)
\(I\) = current (A)
\(A\) = area of the coil (m²)
At equilibrium, the deflection of the pointer is proportional to the current through the coil, within the working range of the instrument.
Main Parts
1. Permanent magnet
2. Moving coil
3. Soft iron core
4. Spring
5. Pointer
6. Scale
7. Terminals
Working
1. Current enters the coil.
2. The current-carrying coil experiences magnetic torque.
3. The coil rotates.
4. The pointer moves across the scale.
5. The spring produces a restoring torque.
6. The pointer stops when the magnetic torque equals the restoring torque.
7. The deflection indicates the magnitude of the current.
Diagram: Moving-Coil Galvanometer
Draw and label:
N and S poles
Permanent magnet
Moving coil
Soft iron core
Spring
Pointer
Scale
Terminals.
---
9. CONVERSION OF A GALVANOMETER
Galvanometer to Ammeter
A galvanometer is converted into an ammeter by connecting a low resistance called a shunt in parallel with it.
\[
\boxed{\text{Galvanometer}+\text{low resistance in parallel}=\text{Ammeter}}
\]
An ammeter has very low resistance and is connected in series in a circuit.
Galvanometer to Voltmeter
A galvanometer is converted into a voltmeter by connecting a high resistance in series with it.
\[
\boxed{\text{Galvanometer}+\text{high resistance in series}=\text{Voltmeter}}
\]
A voltmeter has very high resistance and is connected in parallel across the component whose potential difference is being measured.
---
10. IMPORTANT FORMULAE
Magnetic Force on a Moving Charge
\[
\boxed{F_B=qvB\sin\theta}
\]
For perpendicular motion:
\[
\boxed{F_B=qvB}
\]
Lorentz Force
\[
\boxed{\vec F=q(\vec E+\vec v\times\vec B)}
\]
Electric Force
\[
\boxed{F_E=qE}
\]
Force on a Current-Carrying Conductor
\[
\boxed{F=BIL\sin\theta}
\]
For a perpendicular conductor:
\[
\boxed{F=BIL}
\]
Magnetic Field of a Long Solenoid
\[
\boxed{B=\mu_0nI}
\]
Since:
\[
\boxed{n=\frac{N}{L}}
\]
Then:
\[
\boxed{B=\mu_0\frac{N}{L}I}
\]
Magnetic Torque on a Coil
\[
\boxed{\tau=NBIA}
\]
Ohm's Law
\[
\boxed{V=IR}
\]
Therefore:
\[
\boxed{I=\frac{V}{R}}
\]
and:
\[
\boxed{R=\frac{V}{I}}
\]
Resultant Force
If two forces are perpendicular:
\[
\boxed{F=\sqrt{F_1^2+F_2^2}}
\]
Therefore, for perpendicular electric and magnetic forces:
\[
\boxed{F=\sqrt{F_E^2+F_B^2}}
\]
---
11. WORKED EXAMPLES
Example 1
A proton moves with a velocity of \(3\times10^6,{\rm m,s^{-1}}\) perpendicular to a \(0.2,T\) magnetic field. Calculate the force acting on it.
Given:
\[
q=1.6\times10^{-19}C
\]
\[
v=3\times10^6\,{\rm m\,s^{-1}}
\]
\[
B=0.2T
\]
Since the motion is perpendicular:
\[
F_B=qvB
\]
\[
F_B=(1.6\times10^{-19})(3\times10^6)(0.2)
\]
\[
\boxed{F_B=9.6\times10^{-14}N}
\]
---
Example 2
An electric field of \(500,{\rm N,C^{-1}}\) and a magnetic field of \(0.1,T\) act on a \(2C\) charge moving at \(4,{\rm m,s^{-1}}\), with the fields arranged such that the electric and magnetic forces are perpendicular. Calculate the resultant force.
Electric force:
\[
F_E=qE
\]
\[
F_E=2(500)=1000N
\]
Magnetic force:
\[
F_B=qvB
\]
\[
F_B=2(4)(0.1)=0.8N
\]
Therefore:
\[
F=\sqrt{F_E^2+F_B^2}
\]
\[
F=\sqrt{1000^2+0.8^2}
\]
\[
\boxed{F\approx1000N}
\]
---
Example 3
A \(2m\) wire carries a current of \(5A\) in a \(0.3T\) magnetic field. Calculate the force when the wire is perpendicular to the field.
\[
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