Problem 2206 - JEE Physics

Question

According to Maxwell, a changing electric field produces (A) emf (B) radiation pressure (C) electric current (D) magnetic field

Step-by-Step Solution

Answer

The correct answer is (D) magnetic field. According to Maxwell's Equations, specifically Faraday's Law, a changing electric field produces a magnetic field.

Step 1: Recall Maxwell's Equations

Maxwell's Equations are a set of four fundamental equations that describe the behavior of electric and magnetic fields. In this problem, we focus on the equation that relates a changing electric field to the phenomenon it creates.

Step 2: Identify the Correct Option

According to the third equation of Maxwell (Faraday's Law), a changing electric field produces a magnetic field. Faraday's Law states that the induced electromotive force (EMF) in a closed loop is equal to the rate of change of the magnetic flux through the loop. Mathematically, this can be written as: \( -\frac{d\Phi_B}{dt} = EMF \) Where \(\Phi_B\) is the magnetic flux and t is the time. Now, we look through the given options and match the one that aligns with our understanding of Maxwell's Law: (A) emf - This is the result of a changing magnetic field, not a changing electric field. (B) radiation pressure - This is related to the interaction of electromagnetic waves and matter, not directly to the changing electric field itself. (C) electric current - This can be a result of the induced EMF due to a changing magnetic field, but not directly due to a changing electric field. (D) magnetic field - This is the correct option since a changing electric field produces a magnetic field according to Faraday's Law (part of Maxwell's Equations). The correct answer is (D) magnetic field.

Key Concepts

Faraday's Law

Faraday's Law is a fundamental principle that connects electricity and magnetism. It describes how a changing magnetic field can induce an electromotive force (EMF) in a closed circuit. The basic idea is that as the magnetic environment of a circuit changes, an electrical current is generated or induced in the wire. This phenomenon is captured in the formula:

• \[EMF = -\frac{d\Phi_B}{dt}\]

where \(\Phi_B\) is the magnetic flux, and \(t\) represents time. The negative sign in the equation is crucial as it reflects Lenz's Law, which makes sure the induced EMF creates a current that opposes the change in flux. This principle is what's behind transformers, electric generators, and many other technologies. Understanding Faraday's Law helps us grasp how electric circuits evolve due to magnetic changes. It is one of the key components of Maxwell's Equations, showing the dynamic interplay between electric and magnetic fields.

Electromagnetic fields

Electromagnetic fields are regions around charged particles where electromagnetic forces operate. These fields are composed of electric and magnetic components. They are fundamental to all electromagnetic phenomena. Electric fields are created by stationary charges, while magnetic fields result from moving charges (current). Together, they form an electromagnetic field that propagates through space as waves. The light we see is an example of such a wave.
Maxwell's Equations finely describe how these fields are related and how they behave under varying circumstances.

• Electric fields exert a force on charges, directly influencing their movement.
• Magnetic fields affect any moving charges, altering their trajectory around the field.

These fields have both a direction and magnitude, which can change as the source charge changes. Electromagnetic fields explain everything from how a magnet can attract metals to how smartphones send and receive signals.

Changing Electric Field

A changing electric field is one that varies over time. This change can be due to several factors, such as the movement or variation of charge distribution. Importantly, according to Maxwell's Equations, a changing electric field can induce a magnetic field. This relationship highlights the intrinsic link between electricity and magnetism.
In the context of circuits, a changing electric current can produce varying electric fields, further generating magnetic fields. This is the principle utilized in technologies such as inductors and capacitors.

• An electric field can change due to the displacement of charges or variation in voltage over time.
• These changes compel magnetic fields to form, adapting to the new configuration of the electric field.

Understanding this concept is fundamental in developing technologies like wireless power transmission and advances in electromagnetism.

Magnetic Field Induction

Magnetic field induction is a process where a magnetic field is generated due to the action of a changing electric field. This phenomena is encapsulated in one of Maxwell's Equations and is a cornerstone of modern electromagnetic theory. When electric fields change, they inherently lead to the formation or induction of magnetic fields.
This principle is widely used in engineering and technology.

• Transformers use magnetic induction to transfer energy between circuits through coils.
• Electric motors and generators rely on this process to function effectively.

Induction not only describes the creation of these fields but also the moment-to-moment interaction and evolution of fields in real time. Recognizing how energy can move without physical connections is crucial for modern electrical systems. This understanding is crucial for innovations like magnetic levitation trains and efficient electrical grid designs.