Question

name:
unit 2 lesson 2 worksheet: coulombs law calculation practice

1. two charges of 0.0000001 c and 0.0000002 c are 0.3 m apart.

a) find the force between these two charges.
b) is this force attractive or repulsive?

1. two charges of -0.0000003 and -0.0000006 are 0.8 m apart.

a) find the force between these two charges.
b) is this force attractive or repulsive?

Explanation:

Problem 1a:

Step1: Recall Coulomb's Law

Coulomb's Law is given by \( F = k\frac{|q_1 q_2|}{r^2} \), where \( k = 9\times 10^9 \, \text{N·m}^2/\text{C}^2 \), \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between them.

Step2: Identify the values

\( q_1 = 0.0000001 \, \text{C} = 1\times 10^{-7} \, \text{C} \), \( q_2 = 0.0000002 \, \text{C} = 2\times 10^{-7} \, \text{C} \), \( r = 0.3 \, \text{m} \).

Step3: Substitute into the formula

\[

$$\begin{align*} F&=9\times 10^9\times\frac{|1\times 10^{-7}\times 2\times 10^{-7}|}{(0.3)^2}\\ &=9\times 10^9\times\frac{2\times 10^{-14}}{0.09}\\ &=9\times 10^9\times\frac{2}{9}\times 10^{-12}\\ &=2\times 10^{-3} \, \text{N} \end{align*}$$

\]

Both charges are positive (since \( 0.0000001 \, \text{C} \) and \( 0.0000002 \, \text{C} \) are positive). According to Coulomb's Law, like charges repel each other.

Step1: Recall Coulomb's Law

Coulomb's Law is \( F = k\frac{|q_1 q_2|}{r^2} \), with \( k = 9\times 10^9 \, \text{N·m}^2/\text{C}^2 \).

Step2: Identify the values

\( q_1 = - 0.0000003 \, \text{C} = - 3\times 10^{-7} \, \text{C} \), \( q_2 = - 0.0000006 \, \text{C} = - 6\times 10^{-7} \, \text{C} \), \( r = 0.8 \, \text{m} \). The magnitudes are \( |q_1| = 3\times 10^{-7} \, \text{C} \), \( |q_2| = 6\times 10^{-7} \, \text{C} \).

Step3: Substitute into the formula

\[

$$\begin{align*} F&=9\times 10^9\times\frac{| - 3\times 10^{-7}\times - 6\times 10^{-7}|}{(0.8)^2}\\ &=9\times 10^9\times\frac{18\times 10^{-14}}{0.64}\\ &=9\times 10^9\times 2.8125\times 10^{-13}\\ &=2.53125\times 10^{-3} \, \text{N} \end{align*}$$

\]

Answer:

The force between the two charges is \( 2\times 10^{-3} \, \text{N} \).

Problem 1b: