Problem 44 - Arihant AIEEE Physics

Question

The electric field inside a conductor: (a) must be zero (b) may be non-zero (c) must be non-zero (d) (a) and (c) are correct

Step-by-Step Solution

Answer

(a) must be zero

Step 1: Understanding the Problem

We need to determine the behavior of the electric field inside a conductor. The options given are related to the magnitude of the electric field within the conductor in electrostatic equilibrium.

Step 2: Analyzing Electrostatic Equilibrium

In electrostatic equilibrium, free charges in a conductor move in response to electric fields until the field inside the conductor is zero. This occurs because any non-zero electric field would cause the charges to move, disrupting equilibrium.

Step 3: Applying Concept to the Question

Given the nature of conductors in electrostatic equilibrium, the electric field inside a conductor must be zero. Therefore, option (a) is correct.

Key Concepts

Electrostatic Equilibrium

In electrostatic equilibrium, we're in a state where the electrical forces have balanced out. This means the charges in the system are at rest and there's no net motion. When free charges are present, especially in conductors, they will instinctively rearrange themselves to balance out these forces. Once this rearrangement occurs, no further movement happens because the forces causing movement are gone. The system, thus, achieves equilibrium. A key feature of electrostatic equilibrium is that any field lines are static, and the charges have stopped moving. The interior of a conductor in this state will then have an electric field of zero magnitude. This phenomenon is critical because it highlights a core property of conductors, that is, the absence of electric fields when equilibrium is achieved.

Behavior of Conductors

Conductors are materials that allow the flow of electric charge. They contain free electrons that move easily throughout the material. When we talk about the behavior of conductors, especially under electric fields, it’s crucial to understand how they respond in different states.

• When an external electric field is applied, the free charges in the conductor start to move rapidly, aligning in a way that counteracts the applied field.
• As the charges continue to move, they generate an internal field that precisely cancels out the external field within the conductor. This movement stops only when equilibrium is reached, causing the internal electric field to be zero.

This is why, in electrostatic equilibrium, the electric field inside a perfect conductor must be zero. Conductors swiftly adapt to changes in electric fields, demonstrating their high responsiveness and making them vital in many electrical applications.

Electric Field Magnitude

The electric field magnitude inside a conductor in electrostatic equilibrium is a fundamental concept. The field's magnitude inside a conductor will always adjust to zero when the system reaches equilibrium, for reasons rooted in the fundamental behavior of electric charges.

• If there were any electric field present inside the conductor, it would induce a force on the free charges, causing movement and preventing equilibrium.
• The charges redistribute until they completely cancel the internal field, leading to a net electric field that is zero inside the conductor.

This zero field condition is significant, as it illustrates the conductor's ability to shield its interior from external electric influences. Understanding the zero field inside allows us to exploit conductors in designing devices that manage electrostatic forces effectively.