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?

Options

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Answer 1

Explanation:

The acceleration ‘a’ of charge ‘q’ due tothe fixed charge Q is given by Coulomb’s law:

F = `(kQq)/r^2`

Since acceleration is given by Newton’s second law:

a = `F/m`

= `(kQq)/(mr^2)`

From this equation, we see that acceleration ‘a’ is inversely proportional to r².

So, a is largest when r is the smallest and decreases rapidly as r increases, and the graph should resemble a hyperbola with the form a = `C/r^2`, where C is a constant.