Lenz's Law Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. What is Lenz’s law?

Ans. According to Lenz’s law, in order to ensure that the magnetic flux through the loop is maintained while current runs through it, the generated electromotive force with various polarities produces a current whose magnetic field opposes the change in flux through the loop.

Ques. Is Lenz’s law the same as Faraday’s law?

Ans. No. Faraday's law is concerned with the electromagnetic force produced, whereas Lenz's law is concerned with energy conservation in electromagnetic induction. While Faraday's law provides the magnitude of the emf, Lenz's law specifies the direction of the current. It states that the order always opposes the flux change that generated it.

Ques. What happens if Lenz’s law is reversed?

Ans. If Lenz’s law is reversed, the induced current would create flux in the same direction as the initial change. This more major change in flux would result in a greater current, which would be followed by another more significant change in flux, and so on.

Ques. Write the expression of Lenz’s law.

Ans. According to Lenz’s law, the polarity of induced emf is such that it opposes the cause that produces it. The expression of Lenz’s law is given by

∈ = – N dɸ/dt

Where

• ∈ is the emf induced in the coil
• N is the number of turns in the coil
• dɸ/dt is the rate of change of magnetic flux

Ques. How does Lenz’s law affect generators?

Ans. The direction of produced voltage due to current flow around a loop is represented by Lenz's law. In this case, the voltage drives the current in the opposite direction as the magnetic flux difference around the loop.

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Short Answers Questions [2 Marks Questions]

Ques. Why is Lenz’s law of energy conservation accurate?

Ans. Lenz's law derives from the law of conservation of energy. Energy cannot be created or destroyed, according to the law; it can only be transformed from one form to another. Lenz's law states that the current direction opposes the change in magnetic flux.

Ques. What are the limitations of Lenz’s law?

Ans. The following are the limitations of Lenz’s law

• When a magnet reaches the coil, the external magnetic field generates a current inside the loop, creating a magnetic field inside with a relative magnitude. However, this will come from the opposite direction, limiting the scope of the change.
• When the magnet passes through the coil or any other face of the loop, the current progression adjusts the path. Because of the external magnetic field, the inner magnetic field will be enhanced in a similar manner, opposing the change once more.

Ques. Describe Faraday’s first law of electromagnetic induction.

Ans. The comprehensive investigations of Faraday and Henry provided the foundation for learning about and understanding electromagnetic induction. Based on his experimental discoveries, Faraday concluded that an emf is produced when the magnetic flux across the coil varies over time. As a result, Faraday's first law of electromagnetic induction states that wherever a conductor is placed in a changing magnetic field, an electromotive force is produced. When the conductor circuit is closed, a current is produced known as an induced current.

Ques. What is electromotive force?

Ans. The electric potential formed by changing the magnetic field or using an electrochemical cell is referred to as electromotive force. The term emf stands for electromotive force.

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Long Answers Questions [3 Marks Questions]

Ques. Explain Lenz’s law with the help of all experiments.

Ans. Lenz's law is used to determine the direction of the induced electromotive force and current. Some experiments are listed below.

• First Experiment: In the first experiment, magnetic field lines develop as the current in the coil runs through the circuit. The magnetic flux will increase as the current flowing through the coil increases. When the magnetic flux increases, the induced current would flow in an opposite direction.
• Second Experiment: In the second experiment, an induced current will be produced when the current-carrying coil is wound on an iron rod with its left end acting as an N-pole and is moved in the direction of the coil S.
• Third Experiment: In the third experiment, as the coil pulls towards the magnetic flux, the distance between it and the coil decreases, reducing the coil's surface area inside the magnetic field. When the induced current is applied in the same direction as the motion of the coil, Lenz's law states that the motion is opposed.

Ques. What are the applications of Lenz’s law?

Ans. The following are the applications of Lenz’s law

• Generators and motors: It is used in the construction and operation of motors and generators. In a generator, a wire coil's motion inside a magnetic field causes the coil to conduct electricity. In a motor, the magnetic field produced by the current passing through the coil causes the coil to revolve.
• Transformers: It is used in the construction and use of transformers. A transformer is a tool that modifies an alternating current's voltage. Stepping up or down the voltage is accomplished by using the induced current in the coils of the transformer.
• Eddy current brakes: The design and operation of eddy current brakes use Lenz's law. A device known as an eddy current brake uses a magnetic field to slow down or stop a moving object. An object slows down or stops moving as a result of the magnetic field that is created by the induced current passing through it.
• Magnetic levitation: It is used in the design and operation of magnetic levitation systems. A magnetic field is used in a magnetic levitation device to lift objects. The object levitates because the magnetic field generated by the induced current flowing through it resists gravity.

Ques. What are the significances of Lenz’s law?

Ans. The following are the significance of Lenz’s law

• Lenz's law provides two important details about how a conductor loop will respond to changes in the magnetic field.
• This rule is dependent on the conservation of energy but not the conservation of momentum.
• This law applies to the generation of magnetic fields through wires carrying AC or DC.
• This law relates the direction of an induced current to the rate of change of the induced magnetic field.
• This rule is an essential concept in electromagnetic.

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Very Long Answers Questions [5 Marks Questions]

Ques. A circular coil of radius 10 cm, 500 turns, and resistance 2 Ω is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through 180° in 0.25 s. Estimate the magnitude of the emf and current induced in the coil. (The horizontal component of the earth's magnetic field at that place is 3.0 × 10^-5 T)

Ans. Given

• Radius of the circular coil, r = 10 cm = 10 x 10^-2 m = 10^-1 m
• Number of turns, N = 500
• Resistance of the circular coil, R = 2 Ω
• Duration of rotation of the circular coil, t = 0.25 s
• Horizontal component of the earth's magnetic field, B = 3 x 10^-5 T

Initial magnet flux through the coil is given by

ɸ₁ = BA cosθ₁

⇒ ɸ₁ = B x πr² x cosθ₁

⇒ ɸ₁ = 3 x 10^-5 x 3.14 x 10^-2 x cos0°

⇒ ɸ₁ = 9.42 x 10^-7 Weber

The final magnet flux through the coil is given by

ɸ₂ = BA cosθ₂

⇒ ɸ₁ = B x πr² x cosθ₂

⇒ ɸ₁ = 3 x 10^-5 x 3.14 x 10^-2 x cos180°

⇒ ɸ₁ = - 9.42 x 10^-7 Weber

The emf induced in the coil is given by

∈ = – N dɸ/dt = - N x (ɸ₂ - ɸ₁)/t

On substituting the values, we get

∈ = - 500 x (- 9.42 x 10^-7 - 9.42 x 10^-7)/0.25

⇒ ∈ = 3.8 x 10^-3 V

The induced current in the circuit is given by

I = ∈/R

⇒ I = (3.8 x 10^-3)/2 = 1.9 mA

Ques. A magnetic field of flux density 10 T acts normally on a coil of 50 turns having a 100 cm² area. Find emf induced if the coil is removed from the magnetic field in 0.1 second.

Ans. Given

• The magnitude of the magnetic field acting on the coil, B = 10 T
• The number of turns in the coil, N = 50
• Area of the coil, A = 100 cm² = 10^-2 m²
• Duration in which the coil is removed from the magnetic field, t = 0.1 second

When the coil is in the magnetic field, the magnetic flux linked with the coil is given by

ɸ₁ = NBA cosθ

Where θ is the angle between the direction of the magnetic field and the direction of the area vector of the coil.

On substituting the values and taking θ = 0°, we get

ɸ₁ = 50 x 10 x 10^-2 x cos0°

⇒ ɸ₁ = 5 Weber

When the coil is removed from the magnetic field, the magnitude of the magnetic field becomes zero, therefore the net magnetic flux is given by

ɸ₂ = 50 x 0 x 10^-2 x cos0°

⇒ ɸ₂ = 0

Emf induced in the coil is given by

∈ = – dɸ/dt = -(ɸ₂ - ɸ₁)/t

On substituting the values, we get

∈ = – (0 - 5)/0.1

⇒ ∈ = 50 V

Ques. The magnetic flux through a coil varies according to the relation ɸ = (4t³ + 5t² + 8t^-3 + 5) Weber Calculate the induced current through the coil at t = 2 s if the resistance of the coil is 3.1 ohm.

Ans. Given 

• The resistance of the coil, R = 3.1 ohm
• Time, t = 2 seconds

The variation of magnetic flux through the coil with time as

ɸ = (4t³ + 5t² + 8t^-3 + 5) Weber

On differentiating the above equation with respect to time t, we get

dɸ/dt = d/dt (4t³ + 5t² + 8t^-3 + 5)

⇒ dɸ/dt = 12t² + 10t - 24t^-4 + 5

The emf induced in the coil is given by

|∈| = |- dɸ/dt|t = 2

⇒ |∈| = |12t² + 10t - 24t^-4 + 5|_{t = 2}

⇒ |∈| = |12x 2² + 10x 2 - 24 x 2^-4 + 5|

⇒ |∈| = 66.5 V

The induced current in the circuit is given by

I = ∈/R

⇒ I = 66.5/3.1 = 21.45 A

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