10.4 Electric Forces and Free-Body Diagrams

• The electric force is a vector
• Coulomb's Law states that the electric force is inversely proportional to the square of the distance
• The type of electric force can be either attractive or repulsive.

  True
• Like charges result in a repulsive force.


  True
• Coulomb's constant is represented by the letter k.
• A vector quantity has both magnitude and direction
• The constant in the formula for gravitational force is denoted by G
• What is the value of Coulomb's constant $k$?


  $8.9875 \times 10^{9} \, Nm^{2} / C^{2}$
• Gravitational force is always attractive.


  True
• The superposition principle states that the total electric force on a charge is the vector sum of the individual electric forces.


  True
• Free-body diagrams are more detailed than simple force diagrams as they include all forces and their relative magnitudes.
• The type of electric force depends on the signs of the charges involved.

  True
• In a free-body diagram of a box on a table, the gravitational force acts downward
• Match the charge combination with the type of electric force:

  Like charges (+/+ or -/-) ↔️ Repulsive

  Unlike charges (+/-) ↔️ Attractive
• Steps to calculate the net electric force using the superposition principle:

  1️⃣ Identify all charges in the system

  2️⃣ Calculate individual electric forces using Coulomb's Law

  3️⃣ Vectorially add the forces
• Steps to draw a free-body diagram:

  1️⃣ Isolate the object of interest

  2️⃣ Identify all forces acting on the object

  3️⃣ Represent forces with arrows

  4️⃣ Draw arrows from the object

  5️⃣ Label the forces
• In an FBD of a positive charge between two negative charges, the electric forces are directed towards the negative
• In a free-body diagram, the length of each arrow represents the magnitude of the force.


  True
• Electric forces are calculated using Coulomb's law, which states that $F =$$k \frac{|q_{1} q_{2}|}{r^{2}}$, where $r$ represents the distance
• Electric force can be attractive or repulsive
• Match the type of equilibrium with its characteristic:

  Stable ↔️ Returns to original position

  Unstable ↔️ Moves away from original position

  Neutral ↔️ Remains in new position
• What type of force exists between like charges?

  Repulsive
• Unlike charges (+/-) experience a repulsive force.
• Match the feature with the correct force:

  Charge (q) ↔️ Electric Force

  Mass (m) ↔️ Gravitational Force

  k ↔️ Coulomb's Constant

  G ↔️ Gravitational Constant
• The superposition principle states that the total electric force on a charge is the scalar sum of individual electric forces.

  False
• Steps to draw a free-body diagram:

  1️⃣ Isolate the object

  2️⃣ Identify all forces acting on the object

  3️⃣ Represent forces with arrows

  4️⃣ Draw arrows from the object
• Steps to draw a free-body diagram

  1️⃣ Identify the object

  2️⃣ Identify the forces

  3️⃣ Draw the forces as arrows

  4️⃣ Label the forces
• What are the charges and locations of the three charges in the example provided?

  +2 C at origin, -3 C at (1m,0), +4 C at (0,1m)
• In a free-body diagram, the length of the force arrow should be proportional to its magnitude.


  True
• The formula for calculating electric force using Coulomb's law is F = k \frac{|q_{1} q_{2}|}{r^{2}}</latex>
• Electric force can be either attractive or repulsive, while gravitational force is always attractive


  True
• Match the type of equilibrium with its characteristic:

  Stable ↔️ Returns to original position after displacement

  Unstable ↔️ Moves away from original position after displacement
• Steps to calculate net electric force using free-body diagrams

  1️⃣ Draw the FBD showing all forces

  2️⃣ Calculate individual forces using Coulomb's law

  3️⃣ Vectorially add the forces
• Like charges repel each other.


  True
• Match the factor with its effect on electric force:

  Charges \( q_1 \) and \( q_2 \) ↔️ Larger charges result in stronger force

  Distance \( r \) ↔️ Greater distance results in weaker force
• What is the value of Coulomb's constant in SI units?

  $8.9875 \times 10^{9}$
• What type of force occurs between unlike charges?

  Attractive
• What type of electric force occurs between a positively charged object and a negatively charged object?

  Attractive
• Like charges exert a repulsive force on each other.
• Electric force is significantly stronger than gravitational force.


  True