🧲 Strand C: Gravitational, Electric, and Magnetic Fields

Course: SPH4U — Physics, Grade 12
Focus: Field theory, Coulomb's law, electric circuits, magnetism

1. Gravitational Fields

F_g = Gm₁m₂/r² | g = GM/r² | G = 6.67 × 10⁻¹¹ N·m²/kg²

2. Electric Fields

F_e = kq₁q₂/r² | E = F/q = kQ/r² | k = 8.99 × 10⁹ N·m²/C²

V = kQ/r | ΔV = W/q | E = -ΔV/Δd (uniform field)

3. Magnetic Fields

F = qvB sinθ | F = BIL sinθ | B = μ₀I/(2πr)

Right-hand rules:
• For a straight wire: thumb = current direction, fingers curl = B field direction
• For force on a charge: fingers = v direction, curl toward B, thumb = F direction (positive charge)
• For a solenoid: curl fingers = current direction, thumb = N pole

📝 Worksheet — Strand C: Fields

1. [K/U — 3 marks] Two charges, q₁ = +3.0 μC and q₂ = -5.0 μC, are separated by 0.20 m.

a) Calculate the electric force between them.

b) Is the force attractive or repulsive?

2. [K/U — 3 marks] Calculate the gravitational field strength at a distance of 2 Earth radii from Earth's center (r = 2R_E). Compare to g at the surface.

3. [Thinking — 4 marks] An electron enters a uniform electric field between parallel plates (E = 5000 N/C, plate separation 0.02 m) with horizontal velocity 3.0 × 10⁶ m/s.

a) Calculate the electric force on the electron.

b) Calculate the vertical acceleration.

c) If the plates are 0.10 m long, how much is the electron deflected vertically?

4. [Communication — 3 marks] Compare and contrast gravitational and electric fields. Include: direction of field lines, whether force is always attractive, formula similarities, and relative strength. Present in a table or paragraph.

5. [Application — 4 marks] A proton moving at 5.0 × 10⁶ m/s enters a magnetic field of 0.50 T perpendicular to its velocity.

a) Calculate the magnetic force on the proton.

b) What shape is the proton's path? Why?

c) Calculate the radius of the circular path.

SPH4U — Physics, Grade 12 | Strand C: Fields | Ontario Curriculum 2008