Question

A charge \( Q \) is fixed in position. Another charge \( q \) is brought near charge \( Q \) and released from rest. Which of the following graphs is the correct representation of the acceleration of the charge \( q \) as a function of its distance \( r \) from charge \( Q \)?

• A.
• B.
• C.
• D.

Hint:

For Coulomb’s law, remember the force between two charges is inversely proportional to the square of the distance between them.

Answer 1

The Correct Option is A

The acceleration \( a \) of a charge \( q \) within an electric field generated by a stationary charge \( Q \) is derived via Coulomb's Law. The force \( F \) between these charges is quantified as: \[ F = \frac{k \cdot |Q \cdot q|}{r^2} \] with \( k \) representing Coulomb's constant. Consequently, the acceleration \( a \) of charge \( q \) is determined by: \[ a = \frac{F}{m} = \frac{k \cdot |Q \cdot q|}{m \cdot r^2} \] where \( m \) is the mass of charge \( q \). This equation unequivocally shows that acceleration \( a \) exhibits an inverse square relationship with the distance \( r \). An increase in \( r \) leads to a rapid decrease in \( a \), while a decrease in \( r \) causes a sharp rise in \( a \). Graphically, this relationship is illustrated as a hyperbola of acceleration against distance. Thus, the accurate graphical representation depicts acceleration diminishing proportionally to the inverse square of the distance, corresponding to a \(\frac{1}{r^2}\) relationship. The first graph, demonstrating this inverse square proportionality between acceleration and \( r \), is the correct selection.