Field Scaling and Graphs
Characteristic magnitudes scale as plane r^0, infinite line r^-1, point charge r^-2, and ideal dipole r^-3 in their valid regimes.
Why this shows up in the exam
Matching fields to graphs · Choosing far-field approximations · Identifying source dimension from decay
Learn the idea
Distance laws identify source geometry: ideal plane, line, point, and dipole fields decay differently. Far away, a finite charged object looks like a point charge, while a neutral dipole falls faster. Infinite planes and lines retain their special symmetry laws.
🧠 Memory hook: Plane zero, line one, point two, dipole three powers of distance.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- E_plane proportional to r⁰ — ideal infinite plane
- E_line proportional to r⁻¹ — infinite line
- E_point proportional to r⁻² — localized net charge
- E_dipole proportional to r⁻³ — far field of a neutral dipole
How to approach it
- 1Identify source extent and observation regime
- 2Select the distance exponent
- 3Check limiting behaviour against the graph
Common slip-ups that cost marks
- •Applying a far-field law close to the source
- •Confusing field decay with potential decay
- •Treating finite and infinite sources alike
🌟 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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