Question

Which one of the following statements is not true? a) Equipotential lines are parallel to the electric field lines. b) Equipotential lines for a point charge are circular. c) Equipotential surfaces exist for any charge distribution. d) When a charge moves on an equipotential surface, the work done on the charge is zero.

Short answer

a) Equipotential lines are parallel to the electric field lines. b) Equipotential lines for a point charge are circular. c) Equipotential surfaces exist for any charge distribution. d) When a charge moves on an equipotential surface, the work done on the charge is zero. Answer: a) Equipotential lines are parallel to the electric field lines. Explanation: Equipotential lines are always perpendicular to the electric field lines, not parallel. The electric field lines show the direction of the force on a positive charge, while equipotential lines represent locations where the electric potential is the same. Since the electric field does no work when a charge moves along an equipotential line, it must be perpendicular to the line.

Step-by-step solution

Statement a: Equipotential lines are parallel to the electric field lines.

Equipotential lines are always perpendicular to the electric field lines, not parallel. This is because the electric field lines show the direction of the force on a positive charge, while equipotential lines represent locations where the electric potential is the same. Since the electric field does no work when a charge moves along an equipotential line, it must be perpendicular to the line. Therefore, statement a is not true.

Statement b: Equipotential lines for a point charge are circular.

Equipotential lines for a point charge are indeed circular. This is because the electric potential around a point charge is symmetric and depends only on the distance from the charge. Thus, all points on a circle around the charge will have the same electric potential, making the equipotential lines circular. Statement b is true.

Statement c: Equipotential surfaces exist for any charge distribution.

Equipotential surfaces do exist for any charge distribution. For any given charge distribution, points with the same electric potential can be found, and these points can be connected to create equipotential lines or surfaces. Equipotential surfaces are three-dimensional generalizations of equipotential lines. Statement c is true.

Statement d: When a charge moves on an equipotential surface, the work done on the charge is zero.

When a charge moves on an equipotential surface, it maintains a constant electric potential, so there is no change in its electric potential energy. Since work is the change in potential energy and there is no change in the electric potential energy, the work done on the charge is indeed zero. Statement d is true. #Conclusion# The statement that is not true is statement a: Equipotential lines are parallel to the electric field lines. Equipotential lines are in fact perpendicular to the electric field lines since the electric field does no work when moving a charge along an equipotential line.

Key concepts

Electric Field Lines

Electric field lines are a visual representation used to illustrate the strength and direction of the electric field around charged objects. They originate from positive charges and terminate at negative charges, indicating the path that a positive test charge would take under the influence of the field. The closer these lines are to each other, the stronger the electric field in that region. Understanding the behavior of electric field lines is crucial for visualizing electromagnetic phenomena.
One important characteristic of electric field lines is that they never cross each other. If they did, it would imply two different directions for the electric field at a single point, which is impossible. These lines are an essential tool in the study of electromagnetism as they help to create a mental image of how charged particles interact with each other through the invisible force fields that surround them.

Point Charge

A point charge is an idealized model of a charged particle in which the size of the charge is considered to be infinitesimally small. This model simplifies many complex problems in electrostatics as it allows us to treat charged objects as single points. The electric field created by a point charge is radial, meaning that it extends directly outward or inward from the charge in all directions.
These fields diminish in strength with the square of the distance from the charge, following the inverse-square law. For a positive point charge, the electric field lines radiate outward, while for a negative point charge, the field lines point inward. It's important to understand that real charges have a physical size, but often their dimensions are sufficiently small that treating them as point charges yields a very good approximation in calculations and theoretical work.

Electric Potential

Electric potential, often referred to as voltage, is a measure of the potential energy per unit charge at a point in an electric field. It is a scalar quantity, meaning it has magnitude but no direction. The potential arises due to the position of a charge in an electric field and is a measure of the work done to move a charge from a reference point (usually infinity) to a specific point in the field.
The concept of electric potential is crucial when dealing with electric fields and forces, as it helps to understand how much work is required to move a charge within these fields. Electric potential is also essential for understanding the behavior of charges in circuits, where potential differences between points create the flow of current.

Charge Distribution

Charge distribution refers to the manner in which electric charge is spatially distributed in a material or system. It can be uniform, where the charge density is consistent throughout a region, or it can vary with position. Common types of charge distributions include point charges, lines of charge, surface charges, and volume charges. The specific distribution determines the shape and strength of the resulting electric field and, consequently, the equipotential lines.
Diverse charge distributions produce different electric field configurations. For example, a uniform spherical charge distribution generates a radial electric field outside the sphere, similar to that of a point charge. Understanding the intricacies of charge distribution is essential for not only physics students but also for professionals in fields like electronics and materials science, where electric properties significantly affect the behavior of devices and materials.