Capacitor Energy Formula Selection
For a linear quasistatically charged capacitor, stored field energy is one half QV; substituting Q=CV gives equivalent fixed-V and fixed-Q forms.
Why this shows up in the exam
geometry changes · energy ratios · battery-connected versus isolated comparisons
Learn the idea
Choose the energy form that matches the constrained quantity. The three familiar formulas describe the same stored energy, but one makes a fixed-voltage or fixed-charge change much easier and safer.
🧠 Memory hook: Pick U with the quantity that stays fixed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- U = (1/2)QV — linear capacitor
- U = (1/2)CV² — convenient at fixed V
- U = Q²/(2C) — convenient at fixed Q
How to approach it
- 1State what is fixed
- 2Choose the matching energy formula
- 3Recompute after every configuration change
Common slip-ups that cost marks
- •Using initial Q with final C at fixed V
- •Using initial V after isolation
- •Omitting the one-half factor
🌟 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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