Electric Charge and Coulomb's Law

Types of Electric Charge:
- Positive Charge (Protons)
- Negative Charge (Electrons)
Charge is Quantized:
- Each electron carries a negative charge of
  -e
- Each proton carries a positive charge of
  +e
- Where e = 1.6 imes 10^{-19} ext{ C} (C is a Coulomb)
Interactions of Charges:
- Like charges repel each other
- Opposite charges attract each other
Charge Conservation:
- Electric charge is conserved
- Charge can be moved but cannot be created or destroyed

Key Points:
- The electric force is directed along the line that connects the two charges (charge 1 and charge 2)
- Charges can be considered as “point particles”
- Coulomb’s Law applies to point particles or any object that can be approximated as a point particle
Constants:
- k = 9 imes 10^{9} ext{ Nm}^{2}/ ext{C}^{2}
- ext{ε}_0 = 8.85 imes 10^{-12} ext{ C}^{2}/ ext{Nm}^{2}
Coulomb’s Law Formula:
- The force between two point charges is given by:
  ext{F}{E} = k rac{q1 q_2}{r^2}
  Where:
- ext{F}_{E} is the electric force
- q1 and q2 are the magnitudes of the charges
- r is the distance between the charges

Problem Statement:
- Charge 1 has a charge of +5 ext{ mC} and charge 2 has a charge of +3 ext{ mC}.
- Charge 1 is located at the origin, while charge 2 is located at the position (4 m, 3 m).
- Question: Find the magnitude of the electric force that charge 1 exerts on charge 2.
Choices:
A.) 27000 N
B.) 2755 N
C.) 8438 N
D.) 5400 N
E.) 15000 N
Given Values:
- q_1 = +5 ext{ mC}
- q_2 = +3 ext{ mC}
- Positions:
- Charge 1: (0 m, 0 m)
- Charge 2: (4 m, 3 m)
Coulomb’s Law Application:
ext{F}{E} = k rac{q1 q_2}{r^2}

Problem Statement:
- Similar to Question 1:
- Charge 1 (+5 ext{ mC}) at (0, 0) and Charge 2 (+3 ext{ mC}) at (4, 3).
- Question: Find the direction of the electric force that charge 1 exerts on charge 2 by calculating the angle (theta).
Choices:
A.) 45 deg
B.) 37 deg
C.) 53 deg
D.) 49 deg
E.) 41 deg
Given Parameters:
- Same as Question 1:
- q_1 = +5 ext{ mC}
- q_2 = +3 ext{ mC}
- Position coordinates
Coulomb’s Law Application:
ext{F}{E} = k rac{q1 q_2}{r^2}

Concept:
- Electric forces add like vectors
- Similar to other force calculations learned prior
- For multiple charges: Use Coulomb’s law to find the force from each charge on the charge of interest, then sum the vectors
- Example:
- To find total force on charge qC from charges qA and qB: ext{F}{E ext{ on } C} = ext{F}{E ext{ A on C}} + ext{F}{E ext{ B on C}}

Scenario:
- All charges depicted possess equal magnitude.
- A small positive charge is at the black dot.
- Question: Determine the direction of the net force on this charge.
Choices:
A.) Left
B.) Right
C.) None (forces cancel to zero)

Scenario:
- All charges depicted are of equal magnitude.
- A small positive charge is at the black dot.
- Question: In which cases is the net force on this charge directed to the left?
Choices:
A.) Just A
B.) Just C
C.) Just D
D.) Both A & C
E.) Both A & D

Problem Statement:
- A positive charge of +4q and a negative charge of -q are separated by a distance L.
- Determine possible locations for a positive charge where it would experience zero net electric force.
Choices:
A.) Region I
B.) Region II
C.) Region III
D.) Regions I and III
E.) Regions I, II, and III
- Coulomb’s Law Application:
  ext{F}{E} = k rac{q1 q_2}{r^2}

Scenario:
- A +10 ext{ nC} point charge (charge A) is at the origin, and a +1 ext{ nC} charge (charge C) is placed 1 cm away on the positive x-axis.
- Question: What is the force (magnitude and direction) that charge A exerts on charge C?
Choices:
A.) 9 imes 10^{-4} ext{ N}, ext{ to the left}
B.) 9 imes 10^{-4} ext{ N}, ext{ to the right}
C.) 9 imes 10^{-8} ext{ N}, ext{ to the right}
D.) 9 imes 10^{-6} ext{ N}, ext{ to the left}
E.) 9 imes 10^{-6} ext{ N}, ext{ to the right}
Given Parameters:
- q_A = +10 ext{ nC}
- q_C = +1 ext{ nC}
- Distance from charge A to charge C: 0 cm to 1 cm
Coulomb’s Law Application:
ext{F}{E} = k rac{q1 q_2}{r^2}

Scenario:
- Charge A at the origin +10 ext{ nC} and charge C at 1 cm away +1 ext{ nC}.
- A third charge, charge B +5 ext{ nC} is placed 2 cm from the origin on the positive x-axis.
- Question: What is the force B exerts on C?
Choices:
A.) 4.5 imes 10^{-4} ext{ N}, ext{ to the left}
B.) 4.5 imes 10^{-4} ext{ N}, ext{ to the right}
C.) 1.125 imes 10^{-4} ext{ N}, ext{ to the right}
D.) 1.125 imes 10^{-4} ext{ N}, ext{ to the left}
E.) 0 ext{ N}
Given Parameters:
- q_B = +5 ext{ nC}
- q_A = +10 ext{ nC}
- q_C = +1 ext{ nC}
- Positions: A (0 cm), C (1 cm), B (2 cm)
Coulomb’s Law Application:
ext{F}{E} = k rac{q1 q_2}{r^2}

Scenario:
- Same as Example 2 with charge A at the origin +10 ext{ nC}, C at 1 cm +1 ext{ nC}, and B at 2 cm +5 ext{ nC}.
- Question: What is the total force that A and B exert on C?
Choices:
A.) 4.5 imes 10^{-4} ext{ N}, ext{ to the left}
B.) 4.5 imes 10^{-4} ext{ N}, ext{ to the right}
C.) 13.5 imes 10^{-4} ext{ N}, ext{ to the right}
D.) 13.5 imes 10^{-4} ext{ N}, ext{ to the left}
E.) 0 ext{ N}
Given Parameters:
- Charges and positions same as in Example 2
Coulomb’s Law Application:
ext{F}{E} = k rac{q1 q_2}{r^2}

Problem:
- A positive charge +4q and a negative charge -q are L apart; find placement for a positive charge Q where net force is zero.
Steps:
1. Draw a diagram with all three charges labeled.
2. Draw the forces acting on +Q.
3. Write down the magnitudes of the forces in terms of defined variables.
4. Set total force to zero and solve for the distance (denoted as x).

Calculated the electric force between two point charges using Coulomb’s Law.
Utilized the superposition of electric forces to:
- Determine the direction of the total electric force on a charge.
- Quantitatively find the total electric force on a charge due to multiple other point charges.