Lenz’s Law and Conservation of Energy MCQ Quiz - Objective Question with Answer for Lenz’s Law and Conservation of Energy - Download Free PDF

The correct answer is Option 1: FB = FD, FA = FC.

Explanation:

Lenz’s Law: The direction of induced current opposes the change causing it.

Magnetic force: Acts only on sides of loop cutting through magnetic field lines, proportional to induced current and magnetic field.

FA and FC represent sides moving perpendicular to the magnetic field and induce equal and opposite currents, thus experiencing equal forces (FA = FC).

FB and FD are equal because both sides enter and leave the magnetic field, cutting equal numbers of magnetic field lines at the same rate (FB = FD).

Hence, the correct ranking: FB = FD, FA = FC.

CONCEPT:

Lenz’s law: 

• When a voltage is generated by a change in magnetic flux, then according to Faraday's law, the polarity of the induced voltage is such that it produces a current whose magnetic field opposes the change which produces it.
• The induced emf is given by the rate of change of magnetic flux linked with the circuit i.e.

\(e=-\frac{d\text{ }\!\!\Phi\!\!\text{ }}{dt}\)

Where dΦ = change in magnetic flux and e = induced e.m.f.

EXPLANATION:

• From above it is clear that the direction of induced e.m.f. can be found by using Lenz's law. Therefore option 4 is correct.

• Lenz's law is the consequence of the law of conservation of energy. 

Additional Information

Amperes law:

• The line integral of the magnetic field around any closed curve is equal to μo times the net current I threading through the area enclosed by the curve.

\(\oint \vec B \cdot \overrightarrow {dl} = {\mu _0}I\)

Ampere’s law in this form is not valid if the electric field at the surface varies with time.

Faraday's Laws of Electromagnetic Induction:

• First law: Whenever the number of magnetic lines of force (magnetic flux) passing through a circuit changes an emf is produced in the circuit called induced emf. The induced emf persists only as long as there is change or cutting of flux.
• Second law: The induced emf is given by the rate of change of magnetic flux linked with the circuit i.e.

\(ε = -N\frac{d\phi}{dt}\)

Fleming Left-hand rule:

• It gives the force experienced by a charged particle moving in a magnetic field or a current-carrying wire placed in a magnetic field.
• It states that "stretch the thumb, the forefinger, and the central finger of the left hand so that they are mutually perpendicular to each other.
• If the forefinger points in the direction of the magnetic field, the central finger points in the direction of motion of charge, then the thumb points in the direction of force experienced by positively charged particles."

Concept:

Lenz's Law:

• Lenz's Law states that the polarity of the induced electromotive force (emf) is such that it produces a current which opposes the change in magnetic flux that caused it.
• This law is a consequence of the law of conservation of energy.
• It is used to determine the direction of induced currents in various electromagnetic situations.

 

Explanation:

Given the options:

• 1) Faraday: Faraday's law of induction states that the induced emf is proportional to the rate of change of magnetic flux, but it does not describe the direction of the induced current.
• 2) Maxwell: Maxwell's equations describe the general laws of electromagnetism, but the specific law related to the direction of induced emf is Lenz's Law.
• 3) Kirchhoff: Kirchhoff's laws deal with the current and voltage in electrical circuits, but not with electromagnetic induction.
• 4) Lenz: Lenz's Law correctly describes the polarity of the induced emf, making it the correct answer.

∴ The correct answer is option 4: Lenz.

Explanation:

Lenz's Law

Definition: Lenz's Law, formulated by Heinrich Friedrich Emil Lenz in 1834, is a fundamental principle in electromagnetism. It states that the direction of the induced current in a closed circuit is such that it opposes the change in magnetic flux that produced it. This law is consistent with the principle of conservation of energy and Newton's third law of motion.

Mathematical Expression: Lenz's Law can be mathematically expressed as part of Faraday's law of electromagnetic induction:

ε = -dΦ/dt

Where:

• ε is the electromotive force (EMF) induced in the circuit.
• Φ is the magnetic flux through the circuit.
• dΦ/dt is the rate of change of magnetic flux.
• The negative sign indicates the direction of the induced EMF opposes the change in magnetic flux.

Working Principle: According to Lenz's Law, when there is a change in the magnetic field within a closed circuit, an EMF is induced in such a direction that it creates a current whose magnetic field opposes the initial change in the magnetic field. This opposition is the key aspect of Lenz's Law, ensuring that the induced current always acts to counteract the change that caused it.

Examples:

• Electromagnetic Braking: In applications like magnetic braking systems, Lenz's Law is utilized to generate opposing magnetic fields that create resistive forces, slowing down the motion of a moving object.
• Induction Heating: In induction heating systems, Lenz's Law ensures that the induced currents generate heat by opposing the change in the magnetic field, effectively heating the material.
• Electric Generators: In electric generators, Lenz's Law governs the direction of the induced current, ensuring the generated EMF opposes the change in magnetic flux as the generator operates.

Lenz's law is based upon the law of conservation of energy. Lenz law states that the induced current always tends to oppose the cause which produce it. So in order to do work against opposing force we have to put extra effort. This extra work leads to periodic change in magnetic flux hence more current is induced. Thus the extra effort is just transformed into electrical energy which is law of conservation of energy.

Lenz’s law:

When a voltage is generated by a change in magnetic flux according to Faraday's law, the polarity of the induced voltage is such that it produces a current whose magnetic field opposes the change which produces it.

The induced emf is given by the rate of change of magnetic flux linked with the circuit i.e.

\(e=-\frac{d\text{ }\!\!\Phi\!\!\text{ }}{dt}\)

Where dΦ = change in magnetic flux and e = induced e.m.f.

EXPLANATION:

• Lenz's law is the consequence of the law of conservation of energy. So option 3 is correct.

• The magnitude of the induced emf is given by Faraday's Laws of Electromagnetic Induction. 
• Faraday's Laws of Electromagnetic Induction: Whenever the number of magnetic lines of force (magnetic flux) passing through a circuit changes an emf is produced in the circuit called induced emf. The induced emf persists only as long as there is a change of flux.

 Concept:

Faraday’s law of electromagnetic induction:

​​Faraday’s Laws of Electromagnetic Induction consist of two laws.

Faraday's first law of electromagnetic induction:

It states Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced

Faraday's second law of electromagnetic induction: 

It states that the induced emf is equal to the rate of change in magnetic flux with respect to time.

Formula-induced emf, \(e=-N\frac{Δ ϕ}{Δ t}\) where N = number of turns, Δ ϕ = BAcosθ = Magnetic flux

Lenz’s law:

•  Lenz’s law depends on the principle of conservation of energy and Newton’s third law.
• It is the most convenient method to determine the direction of the induced current.
• It states that the induced electromotive force with different polarities induces a current whose magnetic field opposes the change in magnetic flux through the loop in order to ensure that the original flux is maintained through the loop when current flows in it.

Applications:

• Eddy current balances
• Metal detectors
• Eddy current dynamometers
• Braking systems on train

Explanation:

• ​During Faraday’s electromagnetic induction experiment the mechanical effort of movement of a magnet near a coil produces electric energy within the coil.
• This phenomenon can be best explained on the basis of Lenz's law.
•  Lenz’s law depends on the principle of conservation of energy and Newton’s third law.

Additional Information

Mutual induction:

• It is defined as the property of the coils that enables it to oppose the changes in the current in another coil.
• With a change in the current of one coil, the flow changes too thus inducing EMF in the other coil

Concept

Lenz’s law: When a voltage is generated by a change in magnetic flux according to Faraday's law, the polarity of the induced voltage is such that it produces a current whose magnetic field opposes the change which produces it.

The induced emf is given by the rate of change of magnetic flux linked with the circuit i.e.

\(e=-\frac{d\text{ }\!\!\Phi\!\!\text{ }}{dt}\)

Where dΦ = change in magnetic flux and e = induced e.m.f.

Explanation:

• In Lenz’s law, the induced emf ‘e’ opposes the change (increase or decrease) in flux. So option 2 is correct.

• The magnitude of the induced emf is given by Faraday's Laws of Electromagnetic Induction. 
• Faraday's Laws of Electromagnetic Induction: Whenever the number of magnetic lines of force (magnetic flux) passing through a circuit changes an emf is produced in the circuit called induced emf. The induced emf persists only as long as there is a change of flux.

CONCEPT:

Lenz's Law:

• According to this law, the emf will be induced in a coil due to a changing magnetic flux in such a way that it will oppose the cause which has produced it.
• This law states that the induced emf in a conductor due to a changing magnetic flux is such that the magnetic field created by the induced emf opposes the change in a magnetic field.

\(\Rightarrow emf=-N\left ( \frac{d\phi}{dt} \right )\)

where N = number of loops and dϕ =  Change in magnetic flux

• The above equation is given by Faraday's law, but the negative sign is a result of Lenz's law.

EXPLANATION:

• We know that when a DC current flows through a coil, a magnetic field gets induced in the coil.
• When coil A in which DC current is flowing is moved towards coil B, then the distance between coil A and coil B will decrease.
• So as the distance between coil A and coil B decreases, and the magnetic field of coil A associated with coil B increases.
• Therefore magnetic flux associated with coil B increases and an emf will get induced in coil B such that it will oppose the cause which has produced it.
• So the coil A and coil B will repel each other so coil A stops moving towards B and the magnetic flux associated with coil B stops changing.
• Hence, option 2 is correct.

CONCEPT:

• Lenz’s law: When a voltage is generated by a change in magnetic flux according to Faraday's law, the polarity of the induced voltage is such that it produces a current whose magnetic field opposes the change which produces it.

The induced emf is given by the rate of change of magnetic flux linked with the circuit i.e.

\(e=-\frac{d\text{ }\!\!\Phi\!\!\text{ }}{dt}\)

Where dΦ = change in magnetic flux and e = induced e.m.f.

• The negative sign say that it opposes the change in magnetic flux which is explained by Lenz law.

EXPLANATION:

• The negative sign represents Lenz’s Law which states that the flux produced opposes the rate of change of flux. So option 4 is correct.
• Amperes law: The line integral of the magnetic field around any closed curve is equal to μo times the net current (I) threading through the area enclosed by the curve.
• Ohm's law: At constant temperature and other physical quantities, the current through a conductor is directly proportional to the potential difference across it.
• Faraday's law gives the formula of the induced emf but the sign is given by Lenz law.

• The magnitude of the induced emf is given by Faraday's Laws of Electromagnetic Induction. 
• Faraday's Laws of Electromagnetic Induction: Whenever the number of magnetic lines of force (magnetic flux) passing through a circuit changes an emf is produced in the circuit called induced emf. The induced emf persists only as long as there is a change of flux.

CONCEPT:

• Lenz’s law: When a voltage is generated by a change in magnetic flux according to Faraday's law, the polarity of the induced voltage is such that it produces a current whose magnetic field opposes the change which produces it.
• The induced emf is given by the rate of change of magnetic flux linked with the circuit i.e.

\(e=-\frac{d\text{ }\!\!\Phi\!\!\text{ }}{dt}\)

Where dΦ = change in magnetic flux and e = induced e.m.f.

• The negative sign say that it opposes the change in magnetic flux which is explained by Lenz law.

EXPLANATION:

• Lenz's law is the consequence of the law of conservation of energy. So option 3 is correct.

CONCEPT:

• Lenz’s law: When a voltage is generated by a change in magnetic flux according to Faraday's law, the polarity of the induced voltage is such that it produces a current whose magnetic field opposes the change which produces it.
• The induced emf is given by the rate of change of magnetic flux linked with the circuit i.e.

\(e=-\frac{d\text{ }\!\!\Phi\!\!\text{ }}{dt}\)

Where dΦ = change in magnetic flux and e = induced e.m.f.

• The negative sign say that it opposes the change in magnetic flux which is explained by Lenz law.

EXPLANATION:

• Lenz's law is the consequence of the law of conservation of energy. So option 1 is correct.

Concept:

Bar magnet:

• It is a rectangular piece of an object that shows permanent magnetic properties and is made from a ferromagnetic substance.

​

Magnetic flux:

• Magnetic flux is a measurement of the total magnetic field which passes through a given area.

Lenz law:

• Lenz’s law depends on the principle of conservation of energy and Newton’s third law.
• It is the most convenient method to determine the direction of the induced current.
• It states that the direction of an induced current is always such to oppose the change in the circuit or the magnetic field that produces it.

Explanation:

• ​As the magnet falls the flux through the ring changes.
• Regardless of whether the flux increases or decreases, by Lenz's law a current is induced in the ring that opposes the change in flux.
• This induced current induced a magnetic field that interacts with the falling magnet and decreases the acceleration of fall below g.
• Hence, the acceleration of the falling magnet while passing through the ring is less than the acceleration due to gravity.

CONCEPT:

Lenz’s law: 

• When a voltage is generated by a change in magnetic flux, then according to Faraday's law, the polarity of the induced voltage is such that it produces a current whose magnetic field opposes the change which produces it.
• The induced emf is given by the rate of change of magnetic flux linked with the circuit i.e.

\(e=-\frac{d\text{ }\!\!\Phi\!\!\text{ }}{dt}\)

Where dΦ = change in magnetic flux and e = induced e.m.f.

EXPLANATION:

• From above it is clear that the direction of induced e.m.f. can be found by using Lenz's law. Therefore option 4 is correct.

• Lenz's law is the consequence of the law of conservation of energy. 

Additional Information

Amperes law:

• The line integral of the magnetic field around any closed curve is equal to μo times the net current I threading through the area enclosed by the curve.

\(\oint \vec B \cdot \overrightarrow {dl} = {\mu _0}I\)

Ampere’s law in this form is not valid if the electric field at the surface varies with time.

Faraday's Laws of Electromagnetic Induction:

• First law: Whenever the number of magnetic lines of force (magnetic flux) passing through a circuit changes an emf is produced in the circuit called induced emf. The induced emf persists only as long as there is change or cutting of flux.
• Second law: The induced emf is given by the rate of change of magnetic flux linked with the circuit i.e.

\(ε = -N\frac{d\phi}{dt}\)

Fleming Left-hand rule:

• It gives the force experienced by a charged particle moving in a magnetic field or a current-carrying wire placed in a magnetic field.
• It states that "stretch the thumb, the forefinger, and the central finger of the left hand so that they are mutually perpendicular to each other.
• If the forefinger points in the direction of the magnetic field, the central finger points in the direction of motion of charge, then the thumb points in the direction of force experienced by positively charged particles."

CONCEPT:

Lenz's Law:

• According to this law, the emf will be induced in a coil due to a changing magnetic flux in such a way that it will oppose the cause which has produced it.
• This law states that the induced emf in a conductor due to a changing magnetic flux is such that the magnetic field created by the induced emf opposes the change in a magnetic field.

\(\Rightarrow emf=-N\left ( \frac{d\phi}{dt} \right )\)

where N = number of loops and dϕ =  Change in magnetic flux

• The above equation is given by Faraday's law, but the negative sign is a result of Lenz's law.

EXPLANATION:

• The Lenz law states that the induced emf in a conductor due to a changing magnetic flux is such that the magnetic field created by the induced emf opposes the change in a magnetic field.
• So the direction of induced emf during electromagnetic induction is given by Lenz's law. Hence, option 2 is correct.

Additional Information

Faraday's first law of electromagnetic induction:

• Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced. If the conductor circuit is closed, a current is induced which is called an induced current

​Faraday's second law of electromagnetic induction:

• The induced emf in a coil is equal to the rate of change of flux linked with the coil.

Amperes law: 

• The line integral of the magnetic field around any closed curve is equal to μo times the net current I threading through the area enclosed by the curve.​​​
• \(\oint \vec B \cdot \overrightarrow {dl} = {\mu _0}I\)
• And this equation was modified by Maxwell by incorporating the reverse current or displacement  current (ID) we get Ampere – Maxwell Law
• \(\oint \vec B \cdot \overrightarrow {dl} = {\mu _0}I + {\mu _0}{\epsilon_0}\left( {\frac{{d{{\rm{\Phi }}_E}}}{{dt}}} \right)\)​​
• Where, ​​ \({\epsilon_0}\left( {\frac{{d{{\bf{\Phi }}_E}}}{{dt}}} \right)\)is the displacement current.