Draw a plot showing the variation of (i) electric field (E) and (ii) electric potential (V) with distance r due to a point charge Q.

To illustrate the variation of the electric field (E) and electric potential (V) with distance (r) from a point charge (Q), we can break this down into two distinct concepts: how the electric field behaves as you move away from the charge and how the electric potential changes in that same space. Let’s tackle both aspects step by step.

Electric Field (E) Due to a Point Charge

The electric field created by a point charge can be described using the formula:

• E = k * |Q| / r²

Here, k is Coulomb's constant (approximately 8.99 x 10⁹ N·m²/C²), Q is the magnitude of the charge, and r is the distance from the charge. This formula shows that the electric field strength decreases with the square of the distance from the charge. As you move further away from the charge, the effect of the charge diminishes rapidly.

Graph of Electric Field (E) vs. Distance (r)

If we were to plot this relationship, the x-axis would represent the distance (r), while the y-axis would depict the electric field strength (E). The graph would demonstrate a hyperbolic decline, starting high when close to the charge and approaching zero as you move further away. This inverse square relationship results in a curve that sharply decreases:

• Near the point charge: E is large.
• As r increases: E decreases dramatically.

Electric Potential (V) Due to a Point Charge

Now, let’s look at the electric potential, which is defined by the equation:

• V = k * Q / r

In this case, the potential decreases linearly as the distance from the charge increases, but not as steeply as the electric field. Unlike the electric field, which reflects how strong the force would be on a charge placed in the field, the electric potential represents the potential energy per unit charge.

Graph of Electric Potential (V) vs. Distance (r)

• High potential value when r is small.
• A slower decrease as r gets larger.

Visual Summary

To visualize these concepts together, you would see two curves on the same graph:

• The electric field curve (E) drops sharply, illustrating its dependence on r squared.
• The electric potential curve (V) declines more gently, representing a linear relationship with r.

This comparison highlights the differences in how electric field strength and electric potential behave as you move away from a point charge. Both are critical for understanding electric forces and energies in electrostatics.