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This lesson delves into lenz's law, a fundamental principle in electromagnetism that explains the direction of induced current in response to changing magnetic flux. It explores the relationship between lenz's law and faraday's law, providing a clear explanation of how the direction of the induced current opposes the change in flux. The lesson includes illustrative examples, diagrams, and exercises to solidify understanding.
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Physics principles often have deeper implications than what we may initially perceive. Think, for instance, of a universe where Faraday’s law does not apply. Constructing a perpetual motion machine, which has become a long-standing obsession of fictionists and physicists alike, would have been as easy as ABC. In this universe, however, as the physicist David J. Griffiths succinctly stated, “Nature abhors a change in flux.” As you have learned, an induced emf, will generate a current that opposes the change in flux that caused it. If you look close enough, that is, in fact, a demonstration of the Third Law of Motion and the Conservation of Energy from an electromagnetic vantage. Fascinating. In 1834, three years after the publication of Faraday’s law, a geophysicist found a way to explain this phenomenon more accurately. We know it today as Lenz’s law.
dropped through the metal tube?”
Fig. 9.4.1. Lenz’s law activity setup
Faraday’s law has taught us that the negative sign in the equation shows that the direction of the (1) induced electromotive force and current and (2) the change in flux are always in opposite directions. We have also seen how Maxwell’s evaluation has improved Faraday’s law by establishing the symmetry between the magnetic and the electric field. In this lesson, we will derive Faraday’s law to arrive at an easier alternative way to identify the direction of the induced electromotive force. This method is also called Lenz’s law.
How do we determine the direction of a magnetic induction effect using Lenz’s law?
Lenz’s law is particularly beneficial in helping us analyze the effects of induction. It also validates the Law of Conservation of Energy using electromagnetism. It states that: “The magnetic induction effect always opposes its cause.”
Did You Know? Lenz’s law was formulated by the Russian geophysicist Heinrich Friedrich Emil Lenz (pronounced /lentz/). He was renowned for his world expedition to probe the Atlantic, Pacific, and Indian Oceans to investigate the barometric pressure and salinity of seawater.
Recall from your lesson on electromagnetic induction that when a bar magnet is inserted through a solenoid (conducting coil) such as is shown in Fig. 9.4.2 , an electric current will be induced in the coil, resulting in the production of a magnetic field. The direction of this induced current is proven, explained, and demonstrated by Lenz’s experiments on the applications of Faraday’s law.
a changing magnetic flux caused by a varying/non-uniform magnetic field in a stationary circuit, or (3) a combination of both. Lenz’s law predicts the direction of the induced current as follows:
Fig. 9.4.3. Opposition of magnetic force and the induced current
The bar magnet in the activity at the beginning of the lesson is similar to this set-up. It moved slower than the tiny rock because the direction of its magnetic field is hindered by the change in flux of the system as it moves downward.
Four important variables are accounted for to utilize Lenz’s law correctly. They are (1) the
motion of the magnet ; (2) the change in magnetic flux , (3) the induced magnetic
field , and (4) the induced current I. The easiest way to visualize the directions of these variables with respect to each other is through a bar magnet moving along the axis of a conducting loop or solenoid coil, as shown in Fig. 9.4.4. In each of the following cases, the
induced current I (represented by the purple line) generates an induced magnetic field
(represented by the thick blue line). The direction of this field is always in the opposite direction of the change in flux through the conducting loop caused by the motion of the magnet (represented by the green arrow).
Remember In Lenz’s law, it is the direction of the change in flux and not the flux itself that is taken into consideration.
The change in flux will depend on (1) the direction of the magnetic flux (represented by the blue flux lines) and (2) the motion of the magnet. Recall the four conditions for the increase or decrease of magnetic flux that we discussed in Faraday’s law.
Fig. 9.4.4. Directions of induced currents ‘ Remember When the induced magnetic field that opposes the flux change is upward, the induced current produced must be in a counterclockwise direction , as can be seen in Fig. 9.4.4a and Fig. 9.4.4b. On the other hand, when the induced magnetic field that opposes the flux change is downward , the induced current must be in a clockwise direction, as can be seen in Fig. 9.4.4c and Fig. 9.4.4d.
● The negative sign in the Faraday’s law equation shows that the direction of the induced emf and current and the change in flux are always in opposite directions. ● Lenz’s law states that the magnetic induction effect always opposes its cause. ● In the case of a changing magnetic flux in a motionless/stationary circuit, the induced current will generate its own magnetic field around it. This induced current opposes the direction of the change in magnetic flux through the loop. ● For a changing magnetic flux caused by moving conductors , the induced current generated from the moving conductor will have a direction opposite of the conductor’s magnetic-field force. ● When the induced magnetic field that opposes the flux change is upward, the induced current produced must be in a counterclockwise direction. On the other hand, when the induced magnetic field that opposes the flux change is downward , the induced current must be in a clockwise direction. ___________________________________________________________________________________________
A. Identify whether each statement is true or false. If it is false, correct the underlined word or phrase.
___________ 1. Lenz’s law provides an alternative way to predict the magnitude of the induced current.
___________ 2. When the induced magnetic field that opposes the flux change is upward, the induced current produced must be in a clockwise direction.
___________ 3. Lenz’s law states that “the magnetic induction effect always opposes its cause.”
___________ 4. The negative sign in the Faraday’s law equation shows that the induced emf and current always go along the change of magnetic flux in the loop.
___________ 5. The material from which the loop is made does not affect the induced current of the circuit.
___________ 6. In Lenz’s law, only the direction of the magnetic flux is taken into consideration.
___________ 7. When the induced magnetic field that opposes the flux change is upward, the induced current must be in a clockwise direction.
___________ 8. Lenz’s law validates the Law of Conservation of Mass.
___________ 9. Lenz’s law is a qualitative law.
___________ 10. The^ amount^ of^ induced^ current^ that^ opposes^ any^ flux change is inversely proportional to the resistance in the system.
5-6 Decreasing downward
7-8 Increasing upward
9-10 Decreasing downward
Answer the questions below in two or three sentences
Fig. 9.4.5. Wire-over-loop set-up
Fig. 9.4.6. Loop-within-loop setup
Serway, Raymond A. and John W. Jewett, Jr. Physics for Scientists and Engineers with Modern Physics (9th ed). USA: Brooks/Cole, 2014.
Walker, James S. Physics (5th ed). USA: Pearson Education, 2017.
Young, Hugh D., Roger A. Freedman, and A. Lewis Ford. Sears and Zemansky’s University Physics with Modern Physics (13th ed). USA: Pearson Education, 2012.
