Field of an Infinite Line Charge
For line density lambda in a homogeneous medium, E = lambda/(2 pi epsilon r), radial outward for positive lambda and inward for negative lambda.
Why this shows up in the exam
Field near a long wire · Particle orbit around a line charge · Line-and-sheet superposition
Learn the idea
Cylindrical symmetry makes an infinite line's field radial and proportional to 1/r. A coaxial Gaussian cylinder intercepts the same total flux over its curved side; the end caps contribute none because the field lies parallel to them.
🧠 Memory hook: Line field spreads around a cylinder, giving one power of r.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- E = lambda/(2 pi epsilon r) — field magnitude of an infinite line charge
- Q_enclosed = lambda L — charge inside a coaxial Gaussian cylinder
How to approach it
- 1Choose a coaxial Gaussian cylinder
- 2Use only curved-area flux E(2 pi rL)
- 3Set it equal to lambda L/epsilon
Common slip-ups that cost marks
- •Using the point-charge 1/r² law
- •Including flux through cylinder end caps
- •Using total wire charge instead of lambda L
🌟 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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