Question
Grade 12 Physics - Assignment #3 - Electricity
Every Question should be presented in Grass Fromat, which stands for Given, Required, Analysis, Solution, and Statement.
Two small, identical spheres, with an initial charge of +q and -3q, respectively, attract each other with a force of 𝐹𝑒1→ when held a distance r apart. The two spheres are allowed to touch and are then drawn apart to the distance r. Now they repel with a force of 𝐹𝑒2→.
a) Find the ratio 𝐹𝑒1/𝐹𝑒2 of the two forces. Show your work
b) Describe what this ratio means in terms of magnitude and direction of the two forces, 𝐹𝑒1→ and 𝐹𝑒2→.
c) Why do the two spheres attract initially, but repel after they are brought into contact?
d) After the spheres are touched and then separated, what is the new charge on each sphere? Show your work.
e) Draw vector diagrams of the force vectors for both the initial attractive force and the final repulsive force. Clearly indicate the direction and relative magnitude of each.
f) Describe how the direction of the electric force changes from the initial interaction to after the spheres touch and are separated. Explain why this change in direction occurs, using Coulomb’s law and the concept of electric force vectors between like and unlike charges.
g) If one of the spheres were more massive than the other, how would this affect the motion of the spheres during their interaction? Assume the electrostatic forces are the same.
Every Question should be presented in Grass Fromat, which stands for Given, Required, Analysis, Solution, and Statement.
Two small, identical spheres, with an initial charge of +q and -3q, respectively, attract each other with a force of 𝐹𝑒1→ when held a distance r apart. The two spheres are allowed to touch and are then drawn apart to the distance r. Now they repel with a force of 𝐹𝑒2→.
a) Find the ratio 𝐹𝑒1/𝐹𝑒2 of the two forces. Show your work
b) Describe what this ratio means in terms of magnitude and direction of the two forces, 𝐹𝑒1→ and 𝐹𝑒2→.
c) Why do the two spheres attract initially, but repel after they are brought into contact?
d) After the spheres are touched and then separated, what is the new charge on each sphere? Show your work.
e) Draw vector diagrams of the force vectors for both the initial attractive force and the final repulsive force. Clearly indicate the direction and relative magnitude of each.
f) Describe how the direction of the electric force changes from the initial interaction to after the spheres touch and are separated. Explain why this change in direction occurs, using Coulomb’s law and the concept of electric force vectors between like and unlike charges.
g) If one of the spheres were more massive than the other, how would this affect the motion of the spheres during their interaction? Assume the electrostatic forces are the same.
Answers
GPT-4o mini
# Grade 12 Physics - Assignment #3 - Electricity
### a) Find the ratio 𝐹𝑒1/𝐹𝑒2 of the two forces.
**Given:**
- Charge on sphere A, \( q_A = +q \)
- Charge on sphere B, \( q_B = -3q \)
- Initial distance between spheres, \( r \)
- Coulomb's law for force, \( F = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \)
**Required:**
- Ratio \( \frac{F_{e1}}{F_{e2}} \) where \( F_{e1} \) is the attractive force and \( F_{e2} \) is the repulsive force after touching.
**Analysis:**
1. Calculate \( F_{e1} \), the initial attractive force:
\[
F_{e1} = \frac{k \cdot |q \cdot (-3q)|}{r^2} = \frac{k \cdot 3q^2}{r^2}
\]
2. After touching, both spheres share their total charge:
\[
q_{\text{total}} = +q + (-3q) = -2q \quad \text{(total charge)}
\]
\[
\text{Each sphere after touching:} \quad q' = \frac{-2q}{2} = -q
\]
3. Calculate \( F_{e2} \), the final repulsive force:
\[
F_{e2} = \frac{k \cdot |-q \cdot (-q)|}{r^2} = \frac{k \cdot q^2}{r^2}
\]
**Solution:**
\[
\frac{F_{e1}}{F_{e2}} = \frac{\frac{k \cdot 3q^2}{r^2}}{\frac{k \cdot q^2}{r^2}} = \frac{3q^2}{q^2} = 3
\]
**Statement:**
The ratio of the forces is \( \frac{F_{e1}}{F_{e2}} = 3 \).
---
### b) Describe what this ratio means in terms of magnitude and direction of the two forces, 𝐹𝑒1→ and 𝐹𝑒2→.
**Given:** The calculated ratio \( \frac{F_{e1}}{F_{e2}} = 3 \).
**Required:** Explanation of magnitude and direction of \( F_{e1} \) and \( F_{e2} \).
**Analysis:**
1. \( F_{e1} \) is an attractive force acting between opposite charges (+q and -3q). Therefore, its direction is towards each other.
2. \( F_{e2} \) is a repulsive force acting between like charges (-q and -q). Thus, its direction is away from each other.
**Solution:**
The force \( F_{e1} \) is 3 times stronger than \( F_{e2} \) in magnitude, and while \( F_{e1} \) attracts, \( F_{e2} \) repels.
**Statement:**
In terms of magnitude, the attractive force \( F_{e1} \) is three times that of the repulsive force \( F_{e2} \). The direction of \( F_{e1} \) is toward each sphere, while the direction of \( F_{e2} \) is away from each sphere.
---
### c) Why do the two spheres attract initially, but repel after they are brought into contact?
**Given:** Initial charges are different (+q and -3q).
**Required:** Explanation for attraction and subsequent repulsion.
**Analysis:**
1. Attraction occurs because opposite charges attract each other.
2. After contacting, the charges balance (become similar) resulting in their equal charge of -q.
**Solution:**
Attraction happens because of oppositely charged spheres. After touching, they acquire the same charge; like charges repel.
**Statement:**
The spheres initially attract due to opposite charges and repel after contact due to acquiring identical, like charges.
---
### d) After the spheres are touched and then separated, what is the new charge on each sphere? Show your work.
**Given:**
- Initial charges: \( +q \) and \( -3q \)
**Required:** New charges on each sphere.
**Analysis:**
1. Total charge before touching:
\[
q_{\text{total}} = +q (-3q) = -2q
\]
2. Charge after touching:
\[
\text{Each sphere charge after touch:} \quad q' = \frac{-2q}{2} = -q
\]
**Solution:**
Both spheres have a new charge of \( -q \).
**Statement:**
After touching and separating, each sphere has a charge of \( -q \).
---
### e) Draw vector diagrams of the force vectors for both the initial attractive force and the final repulsive force.
**Given:** Initial attractive force and final repulsive force.
**Required:** Representation of force vectors.
**Analysis:**
- **Initial Force \( F_{e1} \)**: Point toward each other (attraction).
- **Final Force \( F_{e2} \)**: Point away from each other (repulsion).
**Solution:**
(Diagram not drawn, describe)
- Force \( F_{e1} \): Arrows pointing toward each other.
- Force \( F_{e2} \): Arrows pointing away from each other and equal in length, showing equal magnitude after touching.
**Statement:**
The attractive force vectors point toward each other, while the repulsive force vectors point away from each other, indicating their respective interactions.
---
### f) Describe how the direction of the electric force changes from the initial interaction to after the spheres touch and are separated. Explain why this change in direction occurs, using Coulomb’s law and the concept of electric force vectors between like and unlike charges.
**Given:** Interaction between unlike and like charges.
**Required:** Explanation of force direction change.
**Analysis:**
1. Initial interaction (unlike charges): Attract due to Coulomb’s law, resulting in forces pointing toward each other.
2. After contact (like charges): Repel due to like charges producing a force that points away.
**Solution:**
The electric force direction changes from attracting to repelling when the charges become of like sign, as per Coulomb’s law where \( F \propto \frac{q_1 \cdot q_2}{r^2} \).
**Statement:**
The direction changes from attraction (unlike charges) to repulsion (like charges) due to the nature of electric forces as described by Coulomb’s law.
---
### g) If one of the spheres were more massive than the other, how would this affect the motion of the spheres during their interaction? Assume the electrostatic forces are the same.
**Given:** One sphere's mass is greater than the other's.
**Required:** Explanation of motion impact.
**Analysis:**
1. The more massive sphere would accelerate less than the less massive sphere under the influence of the same electrostatic force (Newton's second law).
**Solution:**
The motion would be governed largely by the mass difference, resulting in different accelerations but experiencing equal forces.
**Statement:**
The more massive sphere would accelerate less, leading to different motions during the interaction, due to their differing masses under identical electrostatic forces.
### a) Find the ratio 𝐹𝑒1/𝐹𝑒2 of the two forces.
**Given:**
- Charge on sphere A, \( q_A = +q \)
- Charge on sphere B, \( q_B = -3q \)
- Initial distance between spheres, \( r \)
- Coulomb's law for force, \( F = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \)
**Required:**
- Ratio \( \frac{F_{e1}}{F_{e2}} \) where \( F_{e1} \) is the attractive force and \( F_{e2} \) is the repulsive force after touching.
**Analysis:**
1. Calculate \( F_{e1} \), the initial attractive force:
\[
F_{e1} = \frac{k \cdot |q \cdot (-3q)|}{r^2} = \frac{k \cdot 3q^2}{r^2}
\]
2. After touching, both spheres share their total charge:
\[
q_{\text{total}} = +q + (-3q) = -2q \quad \text{(total charge)}
\]
\[
\text{Each sphere after touching:} \quad q' = \frac{-2q}{2} = -q
\]
3. Calculate \( F_{e2} \), the final repulsive force:
\[
F_{e2} = \frac{k \cdot |-q \cdot (-q)|}{r^2} = \frac{k \cdot q^2}{r^2}
\]
**Solution:**
\[
\frac{F_{e1}}{F_{e2}} = \frac{\frac{k \cdot 3q^2}{r^2}}{\frac{k \cdot q^2}{r^2}} = \frac{3q^2}{q^2} = 3
\]
**Statement:**
The ratio of the forces is \( \frac{F_{e1}}{F_{e2}} = 3 \).
---
### b) Describe what this ratio means in terms of magnitude and direction of the two forces, 𝐹𝑒1→ and 𝐹𝑒2→.
**Given:** The calculated ratio \( \frac{F_{e1}}{F_{e2}} = 3 \).
**Required:** Explanation of magnitude and direction of \( F_{e1} \) and \( F_{e2} \).
**Analysis:**
1. \( F_{e1} \) is an attractive force acting between opposite charges (+q and -3q). Therefore, its direction is towards each other.
2. \( F_{e2} \) is a repulsive force acting between like charges (-q and -q). Thus, its direction is away from each other.
**Solution:**
The force \( F_{e1} \) is 3 times stronger than \( F_{e2} \) in magnitude, and while \( F_{e1} \) attracts, \( F_{e2} \) repels.
**Statement:**
In terms of magnitude, the attractive force \( F_{e1} \) is three times that of the repulsive force \( F_{e2} \). The direction of \( F_{e1} \) is toward each sphere, while the direction of \( F_{e2} \) is away from each sphere.
---
### c) Why do the two spheres attract initially, but repel after they are brought into contact?
**Given:** Initial charges are different (+q and -3q).
**Required:** Explanation for attraction and subsequent repulsion.
**Analysis:**
1. Attraction occurs because opposite charges attract each other.
2. After contacting, the charges balance (become similar) resulting in their equal charge of -q.
**Solution:**
Attraction happens because of oppositely charged spheres. After touching, they acquire the same charge; like charges repel.
**Statement:**
The spheres initially attract due to opposite charges and repel after contact due to acquiring identical, like charges.
---
### d) After the spheres are touched and then separated, what is the new charge on each sphere? Show your work.
**Given:**
- Initial charges: \( +q \) and \( -3q \)
**Required:** New charges on each sphere.
**Analysis:**
1. Total charge before touching:
\[
q_{\text{total}} = +q (-3q) = -2q
\]
2. Charge after touching:
\[
\text{Each sphere charge after touch:} \quad q' = \frac{-2q}{2} = -q
\]
**Solution:**
Both spheres have a new charge of \( -q \).
**Statement:**
After touching and separating, each sphere has a charge of \( -q \).
---
### e) Draw vector diagrams of the force vectors for both the initial attractive force and the final repulsive force.
**Given:** Initial attractive force and final repulsive force.
**Required:** Representation of force vectors.
**Analysis:**
- **Initial Force \( F_{e1} \)**: Point toward each other (attraction).
- **Final Force \( F_{e2} \)**: Point away from each other (repulsion).
**Solution:**
(Diagram not drawn, describe)
- Force \( F_{e1} \): Arrows pointing toward each other.
- Force \( F_{e2} \): Arrows pointing away from each other and equal in length, showing equal magnitude after touching.
**Statement:**
The attractive force vectors point toward each other, while the repulsive force vectors point away from each other, indicating their respective interactions.
---
### f) Describe how the direction of the electric force changes from the initial interaction to after the spheres touch and are separated. Explain why this change in direction occurs, using Coulomb’s law and the concept of electric force vectors between like and unlike charges.
**Given:** Interaction between unlike and like charges.
**Required:** Explanation of force direction change.
**Analysis:**
1. Initial interaction (unlike charges): Attract due to Coulomb’s law, resulting in forces pointing toward each other.
2. After contact (like charges): Repel due to like charges producing a force that points away.
**Solution:**
The electric force direction changes from attracting to repelling when the charges become of like sign, as per Coulomb’s law where \( F \propto \frac{q_1 \cdot q_2}{r^2} \).
**Statement:**
The direction changes from attraction (unlike charges) to repulsion (like charges) due to the nature of electric forces as described by Coulomb’s law.
---
### g) If one of the spheres were more massive than the other, how would this affect the motion of the spheres during their interaction? Assume the electrostatic forces are the same.
**Given:** One sphere's mass is greater than the other's.
**Required:** Explanation of motion impact.
**Analysis:**
1. The more massive sphere would accelerate less than the less massive sphere under the influence of the same electrostatic force (Newton's second law).
**Solution:**
The motion would be governed largely by the mass difference, resulting in different accelerations but experiencing equal forces.
**Statement:**
The more massive sphere would accelerate less, leading to different motions during the interaction, due to their differing masses under identical electrostatic forces.