Magnetic Field on a Circular Loop Axis
For an N-turn circular loop of radius R carrying current I, the field at axial distance x is B = mu_0 N I R^2/[2(R^2 + x^2)^(3/2)], directed along the loop axis.
Why this shows up in the exam
Coil-axis field calculations · Helmholtz-coil reasoning · Center-to-axis field ratios
Learn the idea
The axial field of a circular loop is strongest at the center and falls with axial distance. Off-axis components from opposite elements cancel on the symmetry axis, while axial components add. Far away, the loop behaves like a magnetic dipole.
🧠 Memory hook: On the loop axis, transverse pieces cancel and axial pieces add.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- B_axis = mu₀ N I R²/[2(R² + x²)^(3/2)] — field on the symmetry axis of a thin circular loop
- B_center = mu₀ N I/(2R) — axis formula at x = 0
- B_far proportional to 1/x³ — dipole limit when x is much larger than R
How to approach it
- 1Mark R and axial x
- 2Use symmetry to set the field direction
- 3Apply the axis formula and check center or far-field limits
Common slip-ups that cost marks
- •Using inverse square dependence far away
- •Dropping the number of turns
- •Using axial distance in place of sqrt(R²+x²)
🌟 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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