Gravitational Field, Potential, and Gradient
With V(infinity)=0, gravitational potential satisfies g = -grad V and V(B)-V(A) = -integral_A^B g dot dl; a particle of mass m has potential energy U=mV.
Why this shows up in the exam
Recovering potential from a field · Vector-field work calculations · Relating potential and potential energy
Learn the idea
Field is the negative spatial gradient of potential, while potential is work per unit mass. Potential is a scalar landscape; the gravitational field points in the direction of its steepest decrease.
🧠 Memory hook: Field points downhill on the potential map.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- g = -grad V — field from spatial variation of potential
- Delta V = -integral g dot dl — potential difference from the field
- U = m V — potential energy of a test mass
How to approach it
- 1State the zero of potential
- 2Form the dot product along the path
- 3Apply U=mV only after finding potential
Common slip-ups that cost marks
- •Dropping the minus sign
- •Treating potential as a vector
- •Confusing V in J/kg with U in joules
🌟 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.
A satellite moves in a circular orbit where GM = 4 x 10^14 m^3/s^2 and orbital radius is 2 x 10^6 m. Find its orbital speed.
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