Draw a plot showing the variation of electric field E and electric potential V with the distance r for a point charge Q.

To illustrate the relationship between the electric field (E) and electric potential (V) for a point charge (Q), we can describe how these quantities change with distance (r) from the charge.

Understanding Electric Field and Potential

The electric field (E) and electric potential (V) are fundamental concepts in electrostatics. For a point charge, they are defined as follows:

• Electric Field (E): The electric field created by a point charge is given by the formula:

E = k * |Q| / r²

• Electric Potential (V): The electric potential at a distance r from a point charge is given by:

V = k * Q / r

Graphical Representation

When you plot these equations, you will see distinct behaviors:

• The electric field (E) decreases with the square of the distance (r), resulting in a curve that rapidly drops off as you move away from the charge.
• The electric potential (V) decreases linearly with distance (r), approaching zero as you move far away from the charge.

Key Features of the Graphs

On the graph:

• The x-axis represents the distance (r) from the charge.
• The y-axis shows the values of the electric field (E) and electric potential (V).

As you move away from the point charge:

• The electric field (E) starts high and decreases steeply.
• The electric potential (V) starts at a maximum value and decreases more gradually.

This visual representation helps in understanding how the influence of a point charge diminishes with distance, highlighting the difference in their rates of change.