Notes: Coulomb's law
- Application: when there are two or more small charged objects near each other, they exert electrical forces on each other
- F = ke |q1 q2| / r2
- Direction: attraction if sign of q1 is opposite of q2...
- ke = 9.0 × 109 N m2 / C2
Application
- Small charged objects = "point charges"
- Two point charges → each charge experiences a single electrical force
- Three point charges → each charge experiences two electrical forces
- A charge will experience one additional electrical force for each other charge.
F
- MAGNITUDE of electrical force → always positive
- r = distance between objects
q1
- charge of first object ...
- units = C (Coulomb)
- Everyday objects → 10-10 up to 10-5C
Direction
- attraction → force on one charge points straight towards the other
- repulsion → force on one points straight away from the other
- opposite sign example: q1 > 0 and q2 < 0
Example: Coulomb's law
- A plastic rod is charged to -5.0nC.
- The plastic rod is held directly above a piece of confetti with charge +1.0nC, 1.0cm away.
- [diagram]
- What direction is the force of the rod on the confetti?
- What is the magnitude of the force of the rod on the confetti?
- What direction is the force of the confetti on the rod?
- What is the magnitude of the force of the confetti on the rod?
Do first two together
- Attraction or repulsion? (attraction)
- Attracting object is above → force on confetti is upwards
- F = 4.5×10-4N
Second 2
- Can anyone guess direction (down)
- Can anyone guess magnitude? (same)
- Note: Newton's 3rd law → electrical forces between a single pair of charges will always be 'equal and opposite'
Problem: Point Charge Forces
- Show the directions of the two forces on charge A
- Compute the magnitudes of the two forces
- Compute the compute the components of the two forces
- Compute the components of the total force on A
- Compute the magnitude of the total.
- Compute the direction of the total.
Directions
- FBA is a push , so direction = up (θ = 90°)
- FCA is a pull, so it has the same direction as the line from A to C (down and right).
- Line direction (x-component = +7 cm, y-component = -5 cm, θ = atan(-5/7) = 325°)
Magnitudes
- FBA: q1 = -1 nC, qs = -2 nC, r = 5 cm
- FBA = 7.2×10-6 N
- FCA: q1 = -1 nC, q2 = +3 nC, r = sqrt(52 + 72)cm = 8.6 cm
- FCA = 3.65×10-6 N
Components
- FBAx = 0, FBAy = +7.2×10-6 N
- FCAx = +3.0×10-6 N, FCAy = -2.1×10-6 N
- Sum Fx = +3.0×10-6 N, Fy = +5.1×10-6 N
- F = +5.9×10-6N
- θ = -60°
If there's time, repeat for charge B: Directions
- FAB is a push , so direction = down (θ = 270°)
- FCB is a pull, so direction = right (θ = 0°)
Magnitudes
- FAB: q1 = -1 nC, qs = -2 nC, r = 5 cm
- FBA = 7.2×10-6 N - NOTE this is the same as FAB above. Coulomb's law obeys Newton's 3rd law.
- FCB: q1 = -2 nC, q2 = +3 nC, r = 7 cm
- FCA = 1.1×10-5 N
Components
- FABx = 0, FABy = -7.2×10-6 N
- FCBx = +1.1×10-5 N, FCAy = 0
- Sum Fx = +1.1×10-5 N, Fy = -7.2×10-6 N
- F = +1.3×10-5N
- θ = -33°