Orbital Motion in Electrostatic Fields
For a circular orbit, mv^2/r = |q|E(r). In a point-charge field U = kQq/r, and with a central force angular momentum is conserved.
Why this shows up in the exam
Charge orbiting a point charge · Circular motion around a line or cylinder · Energy statements for electrostatic ellipses
Learn the idea
For circular or central-force motion, electric force supplies radial dynamics while energy and angular momentum govern general orbits. Attraction to a point charge mirrors inverse-square gravitational motion, whereas line-charge and cylinder fields produce different radius dependences.
🧠 Memory hook: Set electric force equal to centripetal force; use central-force invariants for noncircular orbits.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- m v²/r = |q| E(r) — circular-orbit radial balance
- U(r) = k Q q/r — point-charge potential energy
- L = m r x v = constant — angular momentum in a central field
How to approach it
- 1Identify the source field E(r)
- 2Apply radial balance for a circle or energy and angular momentum for an orbit
- 3Check attraction and radius dependence
Common slip-ups that cost marks
- •Using point-charge E for a line charge
- •Adding a separate centripetal force
- •Assuming speed is constant on an elliptical orbit
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
Two point charges 1 microC and 2 microC are 1 m apart in vacuum. Take k = 9 x 10^9 SI. Find the force magnitude.
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