Electromagnetism is three-dimensional, and every exam trap lives in a direction. Before any algebra you must agree on which way current points, how to draw vectors leaving the page, and what your right hand is for. This page is the whole contract — learn it once and every module reads the same way.
§01
Conventional current — the arrow the electrons ignore
The current arrow points the way positive charge would flow — a convention fixed a century before anyone knew the movers are negative electrons drifting the opposite way. Both descriptions give identical physics, so we keep the historical arrow. And note: current has direction but is not a vector — currents through a junction add as plain numbers, not tip-to-tail.
Opposite arrows, one physics. Every rule on this page — grip, palm, Lenz — is written for the current arrow.
◦ In wires: electrons, drifting against I. ◦ In electrolytes: + ions one way and − ions the other — both count as current the same way. ◦ In beams: a proton beam's current follows the beam; an electron beam's current points backwards.
§02
⊙ out, ⊗ in — drawing the third dimension
Fields and currents refuse to stay in the plane of the page, so we borrow an archer's-eye view of a dart: flying at you you see its tip — a dot ⊙; flying away you see its tail feathers — a cross ⊗. Any vector — B, v, I — can wear these symbols.
⊙
Out of the page
The dart's tip, coming straight at you.
⊗
Into the page
The tail feathers, sailing away from you.
A region peppered with ⊗ symbols means a uniform field into the page — the standard stage for charged-particle problems.
B AROUND A WIRE · READ THE SYMBOLS
§03
One right hand, three grips
Every direction question in this chapter is answered by your right hand in one of three poses. Left-handers: same hand — the universe insists.
Grip · straight wire
Thumb = I, curled fingers = B
Wrap your hand around the wire, thumb along the current. Your fingers circle exactly the way the field lines circle — that's how the ⊙/⊗ pattern in §02 was read off.
Curl · loop & solenoid
Curled fingers = I, thumb = B
Same hand, swapped jobs. Fingers follow the current around the loop; your thumb spears through the axis giving B — and names the N face. Mnemonic: a face where current runs aNticlockwise is North.
Palm · F = qv×B
Fingers = v, curl into B, thumb = F
Point straight fingers along v, curl them toward B; the thumb gives the force on a positive charge. Negative charge? Compute for +, then flip. Same rule gives F = IL×B on a wire.
CROSS-PRODUCT TRAINER · SET v AND B, PREDICT F
charge q
velocity v (in the page)
field B (through the page)
F = qv×B → {{ fWord }}
Here v ⊥ B, so |F| = qvB. And F ⊥ v always — the magnetic force bends the path but never does work: speed and kinetic energy stay put.
§04
Lenz's law — the minus sign with an attitude
The minus sign in ε = −dΦdt is energy conservation wearing a disguise: whatever change you force on the flux, the induced current arranges itself to fight that change. Approach with a pole and the coil shows you the same pole; retreat and it shows the opposite, clinging on.
MAGNET MEETS COIL
{{ lzCurl }}
{{ lzSense }}
current sense, seen from the magnet
{{ lzHead }}
{{ lzBody }}
{{ lzFlux }}
Either way you pay: the coil repels you coming and drags you going, and the work of pushing past that reluctance is exactly the electrical energy induced.
§05
Walking a circuit — Kirchhoff's sign rules
The loop rule is bookkeeping: pick a walking direction, add every potential change you step across, set the total to zero. Each element has one fixed rule — the signs then take care of themselves, even when you guessed a current backwards (it just comes out negative).
Battery
− → + : gain ε · + → − : lose ε
Crossing from the short bar to the long bar you climb +ε — regardless of which way the current flows. The emf is a property of the cell, not of the traffic.
Resistor
with I : −IR · against I : +IR
Current flows downhill in potential. Walk the same way as I and you drop IR; walk upstream and you climb it.
Capacitor
− plate → + plate : gain QC
The plate the current flows into is the + plate. In steady state no current crosses it — the capacitor branch is an open switch with a voltage on it.
Inductor
ε = −LdIdt
Lenz again, in copper: rising current meets a back-emf, falling current gets a helping push. Walking with I while I grows, you drop L·dI/dt.
§06
Call the direction
Six one-tap questions. No computing — just read the situation and point. Score: {{ qzScore }}/6
Q{{ qz.n }}
{{ qz.q }}
{{ qz.verdict }}
{{ qz.a }}
Recap card — the contract
◦ Current = direction positive charge would move; electrons drift opposite. Not a vector.
◦ ⊙ out of the page, ⊗ into the page — dart tip vs tail feathers.
◦ Grip: thumb I → fingers B (wire). Curl: fingers I → thumb B (loop/solenoid); aNticlockwise face = North.
◦ Palm: fingers v, curl into B, thumb F — for + charge; flip for −. F ⊥ v, so no work done.
◦ Lenz: induced current opposes the change in flux — approach is repelled, retreat is attracted.
◦ Loop rule: − → + across a cell is +ε always; with the current through R is −IR; rising I through L costs L·dI/dt.