Question 2.1: State Coulomb's Law in words.
Coulomb's Law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This force acts along the line connecting the two charges and is attractive if the charges are of opposite signs and repulsive if they are of the same sign.
Question 2.2: Calculate the force of Qx on Qw.
Coulomb's Law is mathematically expressed as:
\[ F = k \frac{|Q_1 \cdot Q_2|}{r^2} \]
where:
- \( F \) is the magnitude of the force between the charges,
- \( k \) is Coulomb's constant, approximately \( 8.99 \times 10^9 , \text{N m}^2/\text{C}^2 \),
- \( Q_1 \) and \( Q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.
Given values:
- \( Q_x = +5 , \text{nC} = 5 \times 10^{-9} , \text{C} \)
- \( Q_w = -14 , \mu\text{C} = -14 \times 10^{-6} , \text{C} \)
- Distance \( r = 20 , \text{cm} = 0.2 , \text{m} \)
Now substitute the values into the formula to calculate the force:
\[ F_{xw} = k \frac{|Q_x \cdot Q_w|}{r^2} \]
\[ F_{xw} = (8.99 \times 10^9) \frac{|5 \times 10^{-9} \cdot (-14 \times 10^{-6})|}{(0.2)^2} \]
\[ F_{xw} = (8.99 \times 10^9) \frac{70 \times 10^{-15}}{0.04} \]
Calculating this gives:
\[ F_{xw} = (8.99 \times 10^9) \cdot (1.75 \times 10^{-12}) \]
\[ F_{xw} \approx 15.7325 , \text{N} \]
Rounded off to three decimal places:
\[ F_{xw} \approx 15.733 , \text{N} \]
Question 2.3: Calculate the force of Qy on Qw.
Using Coulomb's Law again:
Given values:
- \( Q_y = -8 , \text{nC} = -8 \times 10^{-9} , \text{C} \)
- \( Q_w = -14 , \mu\text{C} = -14 \times 10^{-6} , \text{C} \)
- Distance \( r = 30 , \text{cm} = 0.3 , \text{m} \)
Now substitute the values into the formula to calculate the force:
\[ F_{yw} = k \frac{|Q_y \cdot Q_w|}{r^2} \]
\[ F_{yw} = (8.99 \times 10^9) \frac{|(-8 \times 10^{-9}) \cdot (-14 \times 10^{-6})|}{(0.3)^2} \]
\[ F_{yw} = (8.99 \times 10^9) \frac{112 \times 10^{-15}}{0.09} \]
Calculating this gives:
\[ F_{yw} = (8.99 \times 10^9) \cdot (1.2444 \times 10^{-12}) \]
\[ F_{yw} \approx 11.1980 , \text{N} \]
Rounded off to three decimal places:
\[ F_{yw} \approx 11.198 , \text{N} \]
Summary of Answers:
- Q2.1: Coulomb's Law describes how the electrostatic force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
- Q2.2: Force of \( Q_x \) on \( Q_w \): \( F_{xw} \approx 15.733 , \text{N} \)
- Q2.3: Force of \( Q_y \) on \( Q_w \): \( F_{yw} \approx 11.198 , \text{N} \)
1 answer