5.3 Coulomb's Law

Electric force is a fundamental interaction between charged particles. It's the invisible push or pull that makes opposites attract and likes repel. This force follows Coulomb's Law, which tells us how strong it is based on charge size and distance.

Understanding electric force is key to grasping electromagnetism. It explains everything from static cling to lightning strikes. By learning Coulomb's Law, you'll be able to calculate and predict how charged objects interact in various situations.

Electric Force and Coulomb's Law

Electric force and charged particles

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• Electric force fundamental force acts between electrically charged particles
  • Charged particles can be positively (protons) or negatively (electrons) charged
  • Like charges repel each other (two positive charges push away), while opposite charges attract each other (positive and negative charges pull together)
• Strength of electric force depends on magnitude of charges and distance between them
  • Larger charges result in stronger electric force (doubling charge quadruples force)
  • Force decreases as distance between charges increases (doubling distance reduces force to one-fourth)

Coulomb's Law calculations

• Coulomb's Law describes magnitude of electric force between two point charges
  • Formula for Coulomb's Law: $[F](https://www.fiveableKeyTerm:F) = [k](https://www.fiveableKeyTerm:k) \frac{|q_1||q_2|}{[r](https://www.fiveableKeyTerm:r)^2}$
    • $F$ magnitude of electric force (Newtons)
    • $k$ Coulomb's constant, approximately $8.99 \times 10^9 \frac{N \cdot m^2}{C^2}$
    • $|q_1|$ and $|q_2|$ absolute values of charges (Coulombs)
    • $r$ distance between two charges (meters)
• To calculate electric force, substitute given values into formula and solve for $F$
  • Ensure units are consistent (charges in Coulombs, distance in meters)
  • Example: Two charges of +2 µC and -3 µC separated by 5 cm
    1. Convert units (µC to C, cm to m)
    2. Substitute values: $F = (8.99 \times 10^9) \frac{(2 \times 10^{-6})(3 \times 10^{-6})}{(0.05)^2}$
    3. Calculate: $F = 2.16 \times 10^{-3} N$
• Coulomb's Law follows the inverse square law, where the force is inversely proportional to the square of the distance between charges

Direction of electric forces

• Direction of electric force depends on signs of charges involved
  • If both charges have same sign (both positive or both negative), force is repulsive
    • Charges experience force pushing them away from each other (like ends of two magnets)
  • If charges have opposite signs (one positive, one negative), force is attractive
    • Charges experience force pulling them towards each other (opposite ends of two magnets)
• To determine direction of force, consider signs of charges and relative positions
  • Positive charge will be pushed away from another positive charge
  • Negative charge will be pulled towards a positive charge
  • Direction always along line connecting centers of charges

Superposition principle for multiple charges

• Superposition principle states total electric force on charge is vector sum of individual forces exerted by all other charges
  • To find net force on charge, calculate force due to each individual charge and add as vectors
    • Vector addition takes into account both magnitude and direction of forces
    • Net force on charge can be zero if individual forces cancel each other out (forces in opposite directions)
• When applying superposition principle, calculate force between each pair of charges separately
  • Determine magnitude of each force using Coulomb's Law
  • Determine direction of each force based on signs of charges (repulsive or attractive)
• Add individual forces as vectors to find net force on charge of interest
  • Break vectors into components (x and y directions)
  • Add components separately, then find resultant vector
  • Example: Three charges arranged in a line, +2 µC at origin, -4 µC at (3,0), +1 µC at (0,4)
    1. Calculate forces on +2 µC charge due to other two charges
    2. Find x and y components of each force
    3. Add x components, add y components
    4. Find magnitude and direction of resultant force vector

Electric Fields and Permittivity

• Electric field is a region around a charged particle where it exerts an electrostatic force on other charged particles
• Permittivity is a measure of how easily an electric field can be established in a medium
  • Vacuum permittivity (ε₀) is the permittivity of free space, a fundamental constant in electromagnetism
• The strength of the electric field and the electrostatic force are influenced by the permittivity of the medium