Chapter 3.7, Problem 46E

(a)

To determine

To find: the asymptotes of the graph as function of distance two positive charge.

Answer to Problem 46E

  $F=0\text{ and }r=0$ .

Explanation of Solution

Given:

  $F=\frac{k{q}_1{q}_2}{r^2}$ .

Concept used:

An asymptote is a line that a curve approaches, as it heads towards infinity.

The distance between the curve and the asymptote tends to zero as it heads to infinity.

Coulomb law:

  $F=\frac{k{q}_1{q}_2}{r^2}$ .

Calculation:

Like charges repel and unlike charges attract. Coulomb law states that the force $F$ of attraction or repulsion between two charges $q_1\text{ and }{q}_2$ is given by:

  $F=\frac{k{q}_1{q}_2}{r^2}$

Where $k$ is constant and $r$ is the distance between the charges.

Now it has to graph $F$ as function of $r$ for two positive charges is shown in the figure below.

From the above graph, it has the asymptotes of the graph are $F=0\text{ and }r=0$ .

Hence, $F=0\text{ and }r=0$ .

(b)

To determine

To find: the meaning of having asymptote in terms of the problem.

Answer to Problem 46E

  $r\to 0;F=\infty .$

Explanation of Solution

Given:

  $F=\frac{k{q}_1{q}_2}{r^2}$ .

Concept used:

An asymptote is a line that a curve approaches, as it heads towards infinity.

The distance between the curve and the asymptote tends to zero as it heads to infinity.

Coulomb law:

  $F=\frac{k{q}_1{q}_2}{r^2}$ .

Calculation:

If the distance between the two charges is increased then the force $F$ of attraction or repulsion between two charges $q_1\text{ and }{q}_2$ are continuously decreased.

Hence, as $r\to 0;F=\infty .$