Magnetic-Field Graphs and Scaling
Scaling follows the applicable field law: an infinite wire gives B proportional to r^-1, a loop's far axial field gives x^-3, and a uniform-current wire gives B proportional to r inside. Boundary continuity must match the physical model.
Why this shows up in the exam
Selecting correct B-distance plots · Ratio questions without full arithmetic · Checking derived expressions by limits
Learn the idea
Field graphs encode the governing power law, continuity, and geometry before numerical substitution. A graph can reveal whether the source behaves like a wire, loop, solenoid, or distributed current. Slopes and log-log powers are often faster than plugging values.
🧠 Memory hook: Name the geometry, then read its power law.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- B_wire proportional to r⁻¹ — radial scaling outside a long straight wire
- B_loop,far proportional to x⁻³ — far-axis dipole scaling of a current loop
- B_uniform_wire,inside proportional to r — interior scaling for uniform current density
How to approach it
- 1Identify source geometry and region
- 2Write proportional dependence
- 3Check value, slope, and continuity at special points
Common slip-ups that cost marks
- •Choosing a graph from visual shape without boundary checks
- •Confusing inverse-square and inverse-cube laws
- •Extending a near-field formula into its far-field limit incorrectly
🌟 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 charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
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