Connected Conducting Spheres and Charge Sharing
For well-separated spherical conductors joined by a thin wire, V_1=V_2 and Q_1+Q_2 is conserved; mutual influence is neglected in the simple radius rule.
Why this shows up in the exam
spheres brought into contact · surface-density ratios after sharing · charged-drop comparisons
Learn the idea
Connected isolated conductors reach equal potential while total charge is conserved. A wire lets charge flow until both conductors have the same electrical height. Far-apart spheres then carry charge in proportion to their radii.
🧠 Memory hook: Equal potential gives Q proportional to R, not to area.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Q₁/R₁ = Q₂/R₂ — far-separated spheres at equal potential
- Q₁+Q₂=Q_total — isolated connected system
How to approach it
- 1Write equal-potential condition
- 2Write charge conservation
- 3Solve charges before surface densities
Common slip-ups that cost marks
- •Equalizing charge instead of potential
- •Using Q proportional to R squared
- •Ignoring initial total charge or mutual influence
🌟 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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