Chapter 21, Problem 108A

(a)

To determine

The new force between the two charges for the given change.

Answer to Problem 108A

  $\frac{F}{9}$

Explanation of Solution

Given:

Two charges are $q$ and $Q$

Separation between the charges is $r$

Also, $r$ is tripled

Formula used:

The force between the two charges $q$ and $Q$ separated by a distance $r$ can be written as,

  $F=\frac{KqQ}{r^2}$ $\left(1\right)$

Where, $K$ is constant, $K=9.0\times {10}^9{\text{ Nm}}^2/{\text{C}}^{\text{2}}$

Calculation:

The force between the two charges when $r$ is tripled is obtained by substituting $r=3r$ in equation $\left(1\right)$ ,

  $F=\frac{KqQ}{{\left(3r\right)}^2}$

  $=\frac{KqQ}{{\left(3r\right)}^2}$

  $=\frac{KqQ}{9r^2}$

  $=\frac{F}{9}$

Conclusion:

The force between the two charges when $r$ is tripled is $\frac{F}{9}$

(b)

To determine

The new force between the two charges for the given change.

Answer to Problem 108A

  $3F$

Explanation of Solution

Given:

Two charges are $q$ and $Q$

Separation between the charges is $r$

  $Q$ is tripled

Formula used:

The force between the two charges $q$ and $Q$ separated by a distance $r$ can be written as,

  $F=\frac{KqQ}{r^2}$ $\left(1\right)$

Where, $K$ is constant, $K=9.0\times {10}^9{\text{ Nm}}^2/{\text{C}}^{\text{2}}$

Calculation:

The force between the two charges when $Q$ is tripled is obtained by substituting $Q=3Q$ in equation $\left(1\right)$ ,

  $F=\frac{Kq\left(3Q\right)}{r^2}$

  $=\frac{3KqQ}{r^2}$

  $=3F$

Conclusion:

The force between the two charges when $Q$ is tripled is $3F$

(c)

To determine

The new force between the two charges for the given change.

Answer to Problem 108A

  $\frac{F}{3}$

Explanation of Solution

Given:

Two charges are $q$ and $Q$

Separation between the charges is $r$

$r$ and $Q$ is tripled

Formula used:

The force between the two charges $q$ and $Q$ separated by a distance $r$ can be written as,

  $F=\frac{KqQ}{r^2}$ $\left(1\right)$

Where, $K$ is constant, $K=9.0\times {10}^9{\text{ Nm}}^2/{\text{C}}^{\text{2}}$

Calculation:

The force between the two charges when both $r$ and $Q$ is tripled is obtained by substituting $Q=3Q$ and $r=3r$ in equation $\left(1\right)$ ,

  $F=\frac{Kq\left(3Q\right)}{{\left(3r\right)}^2}$

  $=\frac{3KqQ}{9r^2}$

  $=\frac{F}{3}$

Conclusion:

The force between the two charges when both $r$ and $Q$ is tripled is $\frac{F}{3}$ .

(d)

To determine

The new force between the two charges for the given change.

Answer to Problem 108A

  $\frac{F}{2}$

Explanation of Solution

Given:

Two charges are $q$ and $Q$

Separation between the charges is $r$

Also, r and Q is doubled

Formula used:

The force between the two charges $q$ and $Q$ separated by a distance $r$ can be written as,

  $F=\frac{KqQ}{r^2}$ $\left(1\right)$

Where, $K$ is constant, $K=9.0\times {10}^9{\text{ Nm}}^2/{\text{C}}^{\text{2}}$

Calculation:

The force between the two charges when both $r$ and $Q$ is tripled is obtained by substituting $Q=2Q$ and $r=2r$ in equation $\left(1\right)$ ,

  $F=\frac{Kq\left(2Q\right)}{{\left(2r\right)}^2}$

  $=\frac{2KqQ}{4r^2}$

  $=\frac{F}{2}$

Conclusion:

The force between the two charges when both $r$ and $Q$ is tripled is $\frac{F}{2}$ .

(e)

To determine

The new force between the two charges for the given change.

Answer to Problem 108A

  $F$

Explanation of Solution

Given:

Two charges are $q$ and $Q$

Separation between the charges is $r$

Also, $q$ , $r$ and $Q$ is tripled

Formula used:

The force between the two charges $q$ and $Q$ separated by a distance $r$ can be written as,

  $F=\frac{KqQ}{r^2}$ $\left(1\right)$

Where, $K$ is constant, $K=9.0\times {10}^9{\text{ Nm}}^2/{\text{C}}^{\text{2}}$

Calculation:

The force between the two charges when $q$ , $r$ and $Q$ is tripledis obtained by substituting $Q=3Q$

  $r=3r$

$q=3q$ in equation $\left(1\right)$ ,

  $F=\frac{K\left(3q\right)\left(3Q\right)}{{\left(3r\right)}^2}$

  $=\frac{9KqQ}{9r^2}$

  $=F$

Conclusion:

The force between the two charges when $q$ , $r$ and $Q$ is tripledis $F$ .