Equipotential at a great distance from a collection of charges whose total sum is not zero are approximately:
(A) Spheres
(B) Planes
(C) Paraboloids
(D) Ellipsoids
Answer
301.8k+ views
Hint if we draw a surface in such a way that the electric potential is the same at all the points of the surface, it is called equipotential surface. The component of the electric field parallel to as the potential does not change in this direction. Thus, the electric field is perpendicular to the equipotential surface. For a point charge, the electric field is radial and the electric field is radial and the equipotential surface are concentric spheres with centers at the charge.
Complete Step by step solution
In this problem, the collection of charges, whose total sum is not zero, with regard to great distance can be considered as a point charge.
Now we know that the electric potential due to point charges $q$ is given by
$V = {k_e}\dfrac{q}{r}$
Since, ${k_e}$ and $q$ are constant
Therefore, we can write
$V\alpha \dfrac{1}{r}$
This suggests that electric potentials due to point charge are the same for all equidistant points. the locus of these equidistant points, which are at same potential, form a sphere surface.
Hence, the equipotential at a great distance from a collection of charges whose total sum is not zero are spheres.
Option (A) is correct.
Note The work done in moving a charge between two points in an equipotential surface is zero. If a point charge is moved from point \[{V_A}\] to ${V_B}$ in an equipotential surface, then the work done in moving the charge is given by
\[W = q({V_A} - {V_B})\]
As \[({V_A} - {V_B})\] is equal to zero, the total work done is $W = 0$ .
Complete Step by step solution
In this problem, the collection of charges, whose total sum is not zero, with regard to great distance can be considered as a point charge.
Now we know that the electric potential due to point charges $q$ is given by
$V = {k_e}\dfrac{q}{r}$
Since, ${k_e}$ and $q$ are constant
Therefore, we can write
$V\alpha \dfrac{1}{r}$
This suggests that electric potentials due to point charge are the same for all equidistant points. the locus of these equidistant points, which are at same potential, form a sphere surface.
Hence, the equipotential at a great distance from a collection of charges whose total sum is not zero are spheres.
Option (A) is correct.
Note The work done in moving a charge between two points in an equipotential surface is zero. If a point charge is moved from point \[{V_A}\] to ${V_B}$ in an equipotential surface, then the work done in moving the charge is given by
\[W = q({V_A} - {V_B})\]
As \[({V_A} - {V_B})\] is equal to zero, the total work done is $W = 0$ .
Recently Updated Pages
If the magnetizing field on a ferromagnetic material class 12 physics JEE_Main

A point charge is placed at the corner of a cube The class 12 physics JEE_Main

What changes occur if the monochromatic light used class 12 physics JEE_Main

The unit of specific conductance is A Ohm B Ohmmetre class 12 physics JEE_Main

Which lens is used in magnifying glass A Concave lens class 12 physics JEE_Main

Sir C V Raman won the Nobel Prize in which year A 1928 class 12 physics JEE_Main

Trending doubts
JEE Main 2026: Exam Dates, Session 2 Updates, City Slip, Admit Card & Latest News

Understanding the Electric Field of a Uniformly Charged Ring

Electron Gain Enthalpy and Electron Affinity Explained

Derivation of Equation of Trajectory Explained for Students

Understanding Atomic Structure for Beginners

Understanding Uniform Acceleration in Physics

Other Pages
CBSE Class 12 Physics Question Paper 2026: Download SET-wise PDF with Answer Key & Analysis

JEE Advanced Percentile vs Marks 2026: JEE Main Cutoff, AIR & IIT Admission Guide

How to Convert a Galvanometer into an Ammeter or Voltmeter

Hybridisation in Chemistry – Concept, Types & Applications

What Are Current and Potential Difference in Electricity?

What Are Elastic Collisions in One Dimension?

