Problem 135 - A Complete Resource Book in Physics for JEE Main

Question

Assertion: In an uniform electric field, equipotential surfaces must be plane surface. Reason: Electrons move from a region of lower potential to a region of higher potential if electrons start from rest. (A) \(\mathrm{A}\) (B) \(\mathrm{B}\) (C) \(\underline{\mathrm{C}}\) (D) D

Step-by-Step Solution

Answer

The assertion is correct as in a uniform electric field, equipotential surfaces must be plane surfaces. However, the reason provided is unrelated to the assertion as it discusses the motion of electrons in an electric field rather than the geometry and properties of equipotential surfaces. Therefore, the correct answer is (C) C.

Step 1: Assertion

The assertion states that in a uniform electric field, equipotential surfaces must be plane surfaces. To confirm the assertion, we need to understand the meaning of a uniform electric field and an equipotential surface. A uniform electric field is an electric field with constant magnitude and direction everywhere in the field. An equipotential surface is a surface where all the points have the same electric potential. By definition, the electric field is always perpendicular to the equipotential surface. In a uniform electric field, the direction of the electric field is the same everywhere. For all points on an equipotential surface to have the same electric potential in a uniform electric field, they must form a plane that is perpendicular to the field's direction. Therefore, the assertion is correct.

Step 2: Reason

The reason states that electrons move from a region of lower potential to a region of higher potential if they start from rest. This reason is not related to the assertion and does not correctly explain it. The motion of electrons in an electric field and the shape of equipotential surfaces are separate concepts. The assertion is focusing on the geometry and properties of equipotential surfaces in a uniform electric field, whereas the reason is discussing the motion of electrons in an electric field. Since the reason doesn't correctly explain the assertion, we can conclude that the correct answer is: (C) C

Key Concepts

Equipotential Surfaces

In the context of electric fields, an equipotential surface is a fundamental concept. It is a surface over which the electric potential remains constant. Imagine these surfaces as invisible layers in space, where at every point along the surface, the potential is the same.

To visualize this, think of each layer like a sheet of paper stacked in a precise manner. In a uniform electric field, which means the field is consistent in both magnitude and direction, these surfaces are flat planes. This is because all lines of electric force are parallel, resulting in equipotential surfaces that are orthogonal, or perpendicular, to these lines of force.

Considering this perpendicularity is key: it tells us that no work is required to move a charge along an equipotential surface, because the electric force acts across, not along, the surface, maintaining the potential energy consistently.

Electric Potential

Electric potential is another crucial concept, directly linked to the idea of equipotential surfaces. It is defined as the amount of work needed to move a unit positive charge from a reference point, often from infinity, to a specific point in the field, without changing kinetic energy. This work is done against the electric field.

In a uniform electric field, say between two parallel charged plates, the potential changes linearly with distance. The greater the distance from a low potential region, the higher the electric potential due to the work against the field.

Electric potential measurement units are volts, and it’s important to note that while electric field lines indicate the direction of electric force, equipotential surfaces indicate regions of equal electric potential.

Electron Motion

Electrons, being negatively charged particles, naturally move in a manner that reduces their potential energy in an electric field. Specifically, they travel from regions of higher potential to regions of lower potential.

This movement can be counterintuitive, especially when considering positively charged particles, which move towards higher potentials. Electrons, starting from rest, accelerate towards areas of weaker electric potential due to their negative charge, the opposite of the behavior we see with positive charges.

Understanding electron motion within an electric field is vital, as it explains many phenomena in physics and engineering, such as how current flows in circuits or how cathode rays operate in old TV screens.

Electric Field Direction

The direction of an electric field provides crucial insights into the behavior of charges within that field. By definition, the electric field direction is the path along which a positive test charge would move.

In a uniform electric field, the direction remains the same at all points. This consistency allows for a straightforward analysis of the field's effects on charges, such as the paths they will take and the forces they will experience.

A uniform electric field between two plates, for example, causes charged particles to experience a constant force throughout their journey. This predictable force ensures that equipotential surfaces are planes, enabling clear mathematical predictions and practical applications in designing electrical devices and circuits.