# Rank the electric potentials at the four points shown in the figure below from largest to smallest.

Rank the electric potentials at the four points shown in the figure below from largest to smallest. (Use only “>” or “=” symbols. Do not include any parentheses around the letters or symbols.) Please give explanation!

## General guidance

Concepts and reason
The concept used to solve this question is electric potential. First, determine the distance between corresponding charges to the corresponding points by drawing the diagram and then determine the electric potential at point A and B by using the electric potential formula. Later, determine the electric potential at the point and by using the diagram and the electric potential formula.

Fundamentals

Electric potential: The electric potential is defined as the work required to move a unit charge from a reference point to a specified point. The electric potential is defined as, Here, is the electric potential, is the Coulomb constant, is the charge and is the distance between the charged particle to the required point of electric potential.

## Step-by-step

### Step 1 of 2

The total electric potential at any point is calculated as the scalar sum of all potentials due to different charges. Therefore, the electric potential at point A and B can be expressed as, …… (1) Here, and are two charges which have the value of respectively, is the distance of the corresponding point from charge and is the distance of the corresponding point from charge . The electric potential at point A is. Substitute for, for, for and for in equation (1). The electric potential at point B is. Substitute for, for, for and for in equation (1).

Consider the distance between point A and B from charges is . The distance between point A and B from charges is,

### Step 2 of 2

The electric potential at point C is Substitute for, for, for and for in equation (1). The electric potential at point D is Substitute for, for, for and for in equation (1). From the above explanation, it clearly shows that the electric potential at point D is the highest and at point A is the lowest.

The order of the electric potential at the points from largest to smallest is.

The electric potential at a point is directly proportional to the charge on the charged particle and inversely proportional to the distance between the given point and the location of the charged particle. Mathematically,