Magnetism Part 2: Wires, Spectrometers & Induction

Wires, Selectors and the Mass Spectrometer

A current-carrying wire feels $F = BIL\sin\theta$, zero when it lies along the field and greatest when perpendicular; parallel currents attract and antiparallel currents repel. Crossed electric and magnetic fields pass only the speed $v = E/B$, whatever the particle's mass or charge (the velocity selector). In the analyzer field that follows, $r = mv/qB$ turns mass into radius; strictly the spectrometer sorts ions by $m/q$.

Induction

Magnetic flux is $\Phi = BA\cos\theta$ in webers, with $\theta$ measured from the loop's normal. Faraday's law, $|\varepsilon| = N\,\Delta\Phi/\Delta t$, says only a CHANGING flux induces an EMF, by changing $B$, $A$ or $\theta$ (a sliding rod gives $\varepsilon = BLv$; a rotating loop is a generator). Lenz's law is the minus sign: the induced current opposes the change in flux, which is energy conservation. An MRI scanner is a superconducting solenoid whose steady field induces nothing; its switched gradient coils do, which is why implanted wires are a hazard.

Key Takeaways

• Parallel currents attract, the reverse of like charges.
• A velocity selector picks a speed; the radius in the analyzer reads $m/q$.
• A steady flux, however large, induces no EMF; multiply by the turns $N$.