Problem 36 - Master Resource Book in JEE Main Physics

Question

An emf is produced in a coil, which is not connected to an external voltage source. This can be due to [NCERT Exemplar] (a) the coil being in a time varying magnetic field (b) the coil moving in a time varying magnetic field (c) the coil moving in a constant magnetic field (d) the coil is stationary in external spatially varying magnetic field, which does not change with time

Step-by-Step Solution

Answer

The correct options are (a), (b), and (c).

Step 1: Understanding Electromagnetic Induction

Electromagnetic induction refers to the process by which an emf (electromotive force) is induced in a conductor when it experiences a change in magnetic flux. According to Faraday's Law of Electromagnetic Induction, an emf is induced in a coil when there is a change in magnetic flux through the coil.

Step 2: Evaluating Option A

Option (a) states that an emf is produced when the coil is in a time-varying magnetic field. According to Faraday's Law, a time-varying magnetic field implies changing magnetic flux through the coil, which induces an emf. Therefore, option (a) is correct.

Step 3: Evaluating Option B

Option (b) involves the coil moving in a time-varying magnetic field. This situation results in a change of magnetic flux due to both the movement and time variation of the field, leading to induced emf, making this option correct as well.

Step 4: Evaluating Option C

Option (c) suggests the coil is moving within a constant magnetic field. When the coil moves in a constant field, the relative motion between the coil and field changes the flux through the coil, thus inducing emf. Option (c) is also correct.

Step 5: Evaluating Option D

Option (d) indicates the coil is stationary in an external spatially varying magnetic field, which does not change with time. Since the field does not vary with time and the coil is stationary, there is no change in magnetic flux over time within the coil. Therefore, no emf is induced, making this option incorrect.

Key Concepts

Faraday's Law

Faraday's Law is a fundamental principle in electromagnetism that explains how an electromotive force (emf) is induced in a conductor due to a change in magnetic flux. It is this principle that enables the functioning of many electrical devices and systems, such as transformers and electric generators. According to Faraday's Law, the induced emf in a coil is directly proportional to the rate of change of magnetic flux through the coil.
This can be mathematically expressed as: \[ \text{emf} = - \frac{d\Phi}{dt} \] where \( \Phi \) is the magnetic flux through the coil. The negative sign indicates Lenz's Law, highlighting that the induced emf will always oppose the change in magnetic flux. This feedback prevents the system from going into an infinite loop of energy accumulation.

• The law is crucial in understanding how electric currents can be generated by altering magnetic environments.
• It forms the basis for numerous technological applications, providing the groundwork for harnessing electricity from various renewable and non-renewable sources.

Time-Varying Magnetic Field

A time-varying magnetic field is one whose strength or direction changes over time. This dynamic nature is a vital aspect in the study of electromagnetic induction as it directly impacts the magnetic flux.
Such a field can be generated by changing the current in an electromagnet or through the movement of a permanent magnet. When a coil is placed within a time-varying magnetic field, the changes alter the magnetic flux through the coil over time, inducing an emf as described by Faraday's Law.

• If the field grows stronger, the flux increases; if it weakens, the flux decreases.
• Directional changes also influence the total flux experienced by the coil.

This variability provides a mechanism to induce electric currents, which can be utilized in various applications like induction cooking, where changing magnetic fields induce currenct in pots, heating them directly.

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetism, considering the strength and extent of a magnetic field. It represents how much of the magnetic field 'passes through' a given area and is a pivotal concept in understanding electromagnetic induction.
Magnetic flux \( \Phi \) through a surface is given by the equation: \[ \Phi = B \cdot A \cdot \cos(\theta) \] where \( B \) is the magnetic field strength, \( A \) is the area through which the field lines pass, and \( \theta \) is the angle between the field lines and the perpendicular to the surface. By varying any of these factors, the flux can be changed to induce an emf according to Faraday's Law.

• A larger magnetic field or a larger area leads to more flux, enhancing the potential for generated emf.
• Adjusting the orientation (angle \( \theta \)) between the field and the surface can increase or decrease flux as well.

Understanding magnetic flux aids in designing efficient systems to convert kinetic energy into electricity and vice versa, forming the backbone of power generation technologies.