Error Analysis — Common Mistakes in Magnetism — Notes

Mistake	Why It's Wrong	Correct Approach
"Magnetic force does work on a moving charge"	F = qv×B is always perpendicular to v; work = F·ds = 0 since F ⊥ ds	Magnetic force changes direction, never speed; kinetic energy stays constant
"Faster particle has shorter time period in magnetic field"	T = 2πm/(qB) — no velocity in this formula	T is velocity-independent; faster particle traces larger circle in same time
"For ammeter, add high resistance in series"	Series resistance increases total circuit resistance, reducing current dramatically	Ammeter needs PARALLEL shunt (low resistance); voltmeter needs SERIES resistance (high)
"Solenoid field depends on total number of turns N"	B = μ_{0}nI where n = N/L; if L doubles with same N, n halves, B halves	B depends on turns per unit length (n), not total turns
"At the exact centre of a circular loop, the axial formula applies"	Axial formula is B = μ_{0}N $IR^{2}$ /[2( $R^{2}$ + $x^{2}$ )^(3/2)] — at x=0 it gives μ_{0}NI/2R ✓	Use centre formula B = μ_{0}NI/2R directly; verify: axial formula at x=0 gives the same result
"Paramagnetic materials have χ < 0"	χ < 0 is diamagnetic; paramagnetic has small positive χ	Dia: χ < 0 (repelled); Para: χ > 0 small; Ferro: χ >> 0
"Retentivity and coercivity are the same"	Retentivity = residual B at H=0; coercivity = −H needed to bring B to zero	On hysteresis curve: retentivity = y-intercept; coercivity = x-intercept
"Magnetic force between two wires depends on current direction only"	Formula F/l = μ_{0} $I_{1}I_{2}$ /(2πd) gives magnitude; direction depends on current sense	Same direction → attractive; opposite direction → repulsive (verify with right-hand rule)
"Toroid field is zero everywhere outside"	Field is zero outside toroid AND in the central void region (hollow core)	Outside: B = 0; inside toroid ring: B = μ_{0}NI/2πr; in hollow centre: B = 0
"Diamagnetic effect disappears at high temperature"	Diamagnetism is independent of temperature (unlike paramagnetism)	Paramagnetic χ = C/T (decreases with T); diamagnetic χ is temperature-independent