22.2.3 Lenz’s Law
1. Definition
The induced current flows in such a direction that it opposes the change that produces it.
2. Explanation
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| Figure 22.25: Illustration of Lenz’s Law showing induced current directions when a magnet moves toward/away from a coil and when a circuit is switched on or off, demonstrating how induced emf opposes changes in magnetic flux. |
(a) North pole moving towards coil
(i) Consider a magnet moving towards a coil, with the magnetic north pole pointing towards it, as shown in Figure 22.25(a). The coil is a closed circuit.
(ii) Since the magnet approaches the coil, the magnetic flux through the coil increases with time. Consequently, an emf is induced and a current flows through the coil.
(iii) The current produces a magnetic field. In accordance with Lenz’s law, this induced field must oppose the change (i.e. the increase in flux through the coil) that produces it (the induced current/field). Hence, the induced field must hinder the increase in flux through the coil. To do that, the induced field must point towards the north pole of the magnet. In this way, the rate of increase of field strength at the coil will be slowed down.
(iv) In order to produce the induced field pointing in such a direction, the induced current can only flow in the direction as shown in the diagram.
(b) North pole moving away from coil
(i) Consider a magnet moving away from a coil, with the magnetic north pole pointing towards it, as shown in Figure 22.25(b). Now the magnetic flux through the coil decreases with time.
(ii) The induced magnetic field produced by the induced current must oppose the change (i.e. the decrease of flux through the coil) producing it. It must hinder the decrease in flux. To do that, the induced field must point away from the north pole of the magnet. In this way, the rate of decrease of field strength at the coil will be slowed down.
(iii) In order to produce the induced field pointing in such a direction, the induced current can only flow in the direction as shown in the diagram.
(c) Switching on circuit
(i) Consider a coil connected to a battery, and another coil placed near it, as shown in Figure 22.25(c). The planes of both coils face each other. At the moment when the switch is closed, current begins to flow in the circuit and coil, hence producing a magnetic field. Suppose that the field points towards the second coil.
(ii) The magnetic flux through the second coil increases with time. Because of this, a current is induced in the second coil. This current in turn produces a magnetic field.
(iii) The induced field must oppose the change (i.e. the increase in flux) producing it. Applying the same argument mentioned in (a) above, the induced current in the second coil must flow in the direction as shown in the diagram in order to produce a magnetic field pointing in the ‘correct direction’.
Note: When the current in the circuit has reached maximum and becomes constant, the magnetic flux does not change with time any more. Electromagnetic induction does not occur in the second coil. There is no more induced current in the second coil.
(d) Switching off circuit
(i) Refer to the circuit shown in Figure 22.25(d). A constant current flows in the coil which is connected to the battery. The magnetic flux through the second coil does not change with time. Hence, no induced current flows in that coil.
(ii) At the moment when the circuit is switched off, the current starts to decrease. Likewise, the magnetic flux through the second coil begins to decrease.
(iii) The decreasing flux induces a current in the second coil. This current in turn produces a magnetic field. This field must oppose the change (i.e. the decrease in flux) producing it.
(iv) Applying the same argument mentioned in (a) above, the induced current in the second coil must flow in the direction as shown in the diagram.
EXAMPLE 22.16
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| Figure 22.26 Diagram menunjukkan solenoida yang dihubungkan dengan baterai dan rheostat PQ serta sebuah koil di dekatnya. Perubahan arus saat lengan geser R dipindahkan dari P ke Q menyebabkan perubahan fluks magnet, sehingga menginduksi arus pada koil sesuai Hukum Faraday dan Lenz. |
A solenoid is connected to a battery and a rheostat PQ, as shown in Figure 22.26. A coil of wire which forms a closed circuit is held firmly close to one end of the solenoid. A, B and C are three points on the coil. The direction of the current in the solenoid is indicated by the arrows. Explain what will happen in the coil when the sliding arm R of the rheostat is moved from P towards Q.
Answer
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| Figure 22.27 Diagram showing how increasing current in a solenoid increases magnetic flux through a nearby coil, inducing an emf according to Faraday’s Law of Electromagnetic Induction, while the induced current flows in a direction that opposes the change, in accordance with Lenz’s Law. |
(a) The current in the solenoid produces a magnetic field which points to the left, as shown in Figure 22.27(a). The flux of this field passes through the coil.
(b) As R is moved from P to Q, the total resistance of the circuit decreases. Hence, the current in the solenoid increases with time.
(c) The flux linkage through the coil is proportional to the current in the solenoid.
(d) As the current increases, the flux linkage also increases with time.
(e) Since the flux linkage changes with time, an emf is induced in the coil, in accordance with Faraday’s law of electromagnetic induction. An induced current flows in the coil. As a result, a magnetic field is produced by the induced current.
(f) The induced current must flow in such a direction that it opposes the change producing it, in accordance with Lenz’s law.
(g) The change is the increase of flux linkage with time. Hence, the magnetic field produced by the induced current has to point to the right so as to hinder this increase. This is possible only if the induced current flows along ABC, as shown in Figure 22.27(b).
EXAMPLE 22.17
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| Figure 22.28 Rectangular coil placed in a magnetic field perpendicular to the plane of the coil, where the magnetic field increases with time. |
A rectangular coil has 10 turns, size 2.0 cm × 4.0 cm and resistance 1.5 ohm. It is placed inside a magnetic field with its plane perpendicular to the field, as shown in Figure 22.28. The field points perpendicularly out of the page. At a particular instant, the field strength increases at the rate of 50 mT s-1.
(a) Determine the induced current flowing at that instant.
(b) State the flow direction of the induced current.
Answer
(a) Flux linkage
Φ = Nφ
= N(BA cos θ)
Rate of change of flux linkage
dΦ/dt = (NA cos θ) dB/dt
= (10)(2.0 × 4.0 × 10-4)(cos 0°)(+50 × 10-3)
= +4.0 × 10-4 Wb s-1
Induced emf
E = − dΦ/dt
= −4.0 × 10-4 V
Induced current
I = E / R
= 4.0 × 10-4 / 1.5
= 2.7 × 10-4 A
(b)
(i) The induced current produces a magnetic field. This field must oppose the change that produces the current.
(ii) The change is the increase in strength of the magnetic field which points upwards.
(iii) Hence, the induced magnetic field must point downwards so as to hinder this increase, in accordance with Lenz’s law. The current must flow in the clockwise direction in order to produce the induced magnetic field that points downwards.
| Lenz’s Law Summary | |
|---|---|
| Section | Explanation |
| Definition | The induced current flows in such a direction that it opposes the change that produces it. |
| Magnet Moving Toward Coil |
Magnetic flux increases → induced current flows to oppose the increase. Induced magnetic field opposes the approaching magnet. |
| Magnet Moving Away |
Magnetic flux decreases → induced current flows to oppose the decrease. Induced magnetic field tries to maintain the original flux. |
| Switching On Circuit |
Increasing current → increasing magnetic flux in nearby coil → induced current flows to oppose the increase. Induced current stops when current becomes constant. |
| Switching Off Circuit |
Decreasing current → decreasing magnetic flux → induced current flows to oppose the decrease. Induced current disappears when flux becomes constant (zero change). |
| Key Principle | Induced emf and current always act to resist the change in magnetic flux that produces them. |
| Example Insight |
Increasing magnetic field → induced current creates an opposing magnetic field. Direction of current depends on whether flux is increasing or decreasing. |
| Applications of Lenz’s Law | |
|---|---|
| Application | Explanation |
| Magnet and Coil Motion |
When a magnet moves toward or away from a coil, a current is induced. Lenz’s Law determines the direction of the induced current which opposes the change in magnetic flux. |
| Generator |
Mechanical energy is converted into electrical energy. The induced current flows in a direction that opposes the motion producing it. |
| Transformer |
Uses changing current in the primary coil to induce current in the secondary coil. Lenz’s Law ensures the induced current opposes changes in magnetic flux. |
| Induction Braking |
Used in trains and roller coasters. Induced currents produce magnetic forces that oppose motion, slowing the object down. |
| Induction Cooker |
Alternating magnetic fields induce eddy currents in cookware. These currents produce heat due to resistance. |
| Key Principle | All induced currents act to oppose the change in magnetic flux that caused them. |
Lenz’s Law explains that any induced current will always flow in a direction that opposes the change in magnetic flux that produces it. This principle is a direct consequence of the conservation of energy, ensuring that energy is not created or destroyed spontaneously.
In practical applications, Lenz’s Law helps determine the direction of induced current in various situations such as moving magnets, solenoids, transformers, generators, and electromagnetic braking systems. By understanding this law, we can better analyze and predict the behavior of electromagnetic systems.
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