Question

Identify which of the above shown graphs represent the force between two electrons Vs distance between them?

(A) Graph A
(B) Graph B
(C) Graph C
(D) Graph D
(E) Graph E

Answer 1

Hint: The force between the electrons can be determined from the Coulomb’s law of electric charges. This law is also called the inverse square law. Where, the force is inversely proportional to the square of the distance. And the force is also called the electrostatic force.

Complete Step by step solution:
The Coulomb’s law of attraction or repulsion states that the force between two charges will be proportional to the product of magnitude of two charges and inversely proportional to the square of the distance between them.
$F = \dfrac{1}{{4\pi {\varepsilon _0}}}\dfrac{{{q_1}{q_2}}}{{{r^2}}}$
Where, ${q_1}$ and ${q_2}$ are the magnitude of two charge, $r$ is the distance between the two charges and ${\varepsilon _0}$ is the permittivity of free space.
For the force between the two electrons of charge $e$,
$\Rightarrow F = \dfrac{1}{{4\pi {\varepsilon _0}}}\dfrac{{e \times e}}{{{r^2}}}$
It is clear that the force is inversely proportional to the square of the distance between them. When the electrons are far apart, then the force between them will be much smaller. Thus, the force of repulsion is less when they are far. When the distance is small that is if they are near the force of repulsion will be greater. The decrease is not linear. The decrease in force with increase in distance will be exponentially. Hence the graph A shows the decrease in force $F$ with increase in distance $r$.

The answer is option A.

Note: The force is represented in the Y- axis and the distance between the electrons in X- axis where the small increase in distance will bring large decrease in force. Hence, they related to inverse square law. The force is directly proportional to the product of the two charges.