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A charge q of mass m moving at v across a uniform field B: the record `r` = mv/|q|B, `T` = 2πm/|q|B, `f`, `omega` and `sense` ("clockwise" for a positive charge with B out of the page, by the right-hand rule).
q (number) -- the charge (sign kept)m (number) -- the massv (number) -- the speedB (number) -- the fieldv at θ degrees to B: the record `r` = mv sinθ/|q|B, `T`, `pitch` = v cosθ T, `vPerp`, `vPar`.
q (number) -- the chargem (number) -- the massv (number) -- the speedtheta (number) -- the angle between v and B in degreesB (number) -- the fieldCrossed fields E and B: the speed that passes undeflected, v = E/B.
E (number) -- the electric fieldB (number) -- the magnetic fieldThe cyclotron: the record `f` = |q|B/2πm, `T`, `vMax` = |q|BR/m at the exit radius R and `kMax` = q²B²R²/2m in joules.
q (number) -- the chargem (number) -- the massB (number) -- the fieldR (number) -- the dee radiusA charge entering a strip of field of width w at right angles to its edge: the record `r`, `exits` (true when r > w and it leaves the far edge), `deflection` in degrees (sin θ = w/r, or 180 for the U-turn), `sideways` (r(1 - cos θ), or 2r) and `time` in the field.
q (number) -- the chargem (number) -- the massv (number) -- the speedB (number) -- the fieldw (number) -- the strip's widthA long straight wire, B = μ0 I/2πd at distance d; with the two angles θ1 and θ2 (degrees, from the perpendicular to the segment's ends, each positive on its own side) a finite segment, B = μ0 I (sin θ1 + sin θ2)/4πd.
I (number) -- the currentd (number) -- the perpendicular distancetheta1 (number) -- optional: the angle to one endtheta2 (number) -- optional: the angle to the other endAn arc of radius R subtending the given degrees at its centre: B = μ0 I θ/4πR there (360 gives the full loop's μ0 I/2R).
I (number) -- the currentR (number) -- the radiusdegrees (number) -- the angle subtendedN turns of radius R: B on the axis at x, μ0 N I R²/2(R² + x²)^(3/2); at the centre when x is left out.
I (number) -- the currentR (number) -- the radiusN (number) -- the turns (1 unless given)x (number) -- the distance along the axis (0 unless given)Inside a long solenoid: B = μ0 n I for n turns per metre (half that at an end).
n (number) -- the turns per metreI (number) -- the currentInside a toroid of N turns at radius r: B = μ0 N I/2πr.
N (number) -- the total turnsI (number) -- the currentr (number) -- the radius of the circle inside the coreThe field at a point (the origin unless x, y are given) of a current I round a planar shape, positive out of the page: the parts a list of records, an arc `{"kind": "arc", "r", "from", "to"}` about the origin (the current from `from` to `to` degrees, anticlockwise when to > from) and a segment `{"kind": "line", "x1", "y1", "x2", "y2"}` in the current's direction. Each arc gives μ0 I θ/4πR at the origin, each segment μ0 I (sin θ1 + sin θ2)/4πd with the sign by the side the point lies on; a segment through the point gives nothing.
I (number) -- the currentparts (list) -- the arcs and segments in the order the current flowsx (number) -- optional: the point's xy (number) -- optional: the point's yThe parts of a regular n-gon of the given side centred on the origin, the current anticlockwise, a vertex on the +x axis: a list for `wireShapeField` and `wireShapeOn`.
n (number) -- the number of sides, 3 to 64side (number) -- the sideTwo long parallel wires d apart: the record `perLength` = μ0 I1 I2/2πd, `force` on a length L (1 m unless given) and `attract` (true when the currents run the same way).
I1 (number) -- one currentI2 (number) -- the otherd (number) -- the separationL (number) -- the length the force acts on (1 unless given)F = B I L sin θ on a straight conductor (θ = 90 unless given).
I (number) -- the currentL (number) -- the lengthB (number) -- the fieldtheta (number) -- the angle between the conductor and B in degreesA coil of N turns, area A and current I with its normal at θ to B: the record `m` = NIA, `torque` = mB sin θ, `energy` = -mB cos θ, `flux` = NBA cos θ.
N (number) -- the turnsI (number) -- the currentA (number) -- the areaB (number) -- the fieldtheta (number) -- the angle between the normal and B in degreesThe shunt that lets a galvanometer of resistance G and full-scale current Ig read a current I: S = Ig G/(I - Ig).
G (number) -- the galvanometer's resistanceIg (number) -- its full-scale currentI (number) -- the current to readThe series resistor that lets it read a voltage V: R = V/Ig - G.
G (number) -- the galvanometer's resistanceIg (number) -- its full-scale currentV (number) -- the voltage to readA short bar magnet of moment m far away: axial μ0 2m/4πr³, equatorial μ0 m/4πr³ ("axial" unless the word is given).
m (number) -- the magnetic momentr (number) -- the distance from the centrewhere ("axial" or "equatorial") -- which line the point is onA freely pivoted magnet in B: T = 2π sqrt(I/mB).
I (number) -- the moment of inertiam (number) -- the magnetic momentB (number) -- the fieldThe earth's field from its horizontal component and the dip: the record `B` = BH/cos δ and `BV` = BH tan δ.
BH (number) -- the horizontal componentdip (number) -- the dip in degreesemf = B l v for a rod moving across B.
B (number) -- the fieldl (number) -- the rod's lengthv (number) -- the speedemf = B ω l²/2 for a rod turning about one end in B.
B (number) -- the fieldl (number) -- the rod's lengthomega (number) -- the angular speed in rad/sΦ = N B A cos θ through a coil whose normal is at θ to B (the same as loopTorque's `flux`).
N (number) -- the turnsI (number) -- the current (unused, kept for the same order as loopTorque)A (number) -- the areaB (number) -- the fieldtheta (number) -- the angle in degreesA rod of length l sliding at v on rails closed by R in B: the record `emf` = Blv, `current`, `force` = BIl against the motion and `power` = I²R.
B (number) -- the fieldl (number) -- the rod's lengthv (number) -- the speedR (number) -- the resistanceA rectangular loop w wide and h high moving at v along x into a field strip from x = 0 to x = strip, its leading edge at x: the record `inside` (the width inside), `flux` = B h inside, `emf` = Bhv while one edge is in the strip and 0 otherwise, `state` ("outside", "entering", "inside", "leaving", "crossing" for a loop wider than the strip).
strip (number) -- the strip's widthw (number) -- the loop's widthh (number) -- its heightB (number) -- the fieldv (number) -- the speedx (number) -- the leading edge's positionL = μ0 n² A l for a long solenoid of n turns per metre.
n (number) -- the turns per metreA (number) -- the cross-sectionl (number) -- the lengthM = μ0 n1 n2 A l for two coaxial solenoids sharing a length l, the inner one of area A.
n1 (number) -- the turns per metre of onen2 (number) -- of the otherA (number) -- the inner areal (number) -- the shared lengthThe LR circuit: the record `current` at t (growth (V/R)(1 - e^(-t/τ)), or decay (V/R) e^(-t/τ) with the word "decay"), `final` = V/R and `tau` = L/R.
V (number) -- the emfR (number) -- the resistanceL (number) -- the inductancet (number) -- the timemode ("growth" or "decay") -- growth unless givenA rectangle of ⊙ (out) or ⊗ (in) marks for a field through the page, drawn as small circles with a dot or a cross (plain shapes, no font), the box outlined faintly. Sets the ranges to the box when the diagram has none.
d (diagram) -- the diagramx0 (number) -- the left edgey0 (number) -- the bottom edgex1 (number) -- the right edgey1 (number) -- the top edgefield ("in" or "out") -- B through the page: "out" (⊙, +z) or "in" (⊗, -z); out unless givenspacing (number) -- the marks' spacing (a sixth of the longer side unless given)colour (text) -- the marks' colourOne ⊙ or ⊗ mark at a point.
d (diagram) -- the diagramx (number) -- the point's xy (number) -- its yfield ("in" or "out") -- B through the page: "out" (⊙, +z) or "in" (⊗, -z); out unless givensize (number) -- the mark's radius (2% of the view's width unless given)The circular path of a charge in a uniform field through the page: the field marks, the dashed circle of radius mv/|q|B with its sense by the right-hand rule, the charge at the top moving along +x, the v and F arrows, C and r, the caption r, T and the sense (the diagram's summary).
d (diagram) -- the diagramq (number) -- the charge (sign kept)m (number) -- the massv (number) -- the speedB (number) -- the fieldfield ("in" or "out") -- B through the page: "out" (⊙, +z) or "in" (⊗, -z); out unless givenA charge entering a strip of field of width w from the left: the arc inside, then the deflected straight path with θ (sin θ = w/r) when r > w, or the semicircle and the way back out of the entry face 2r along it when r ≤ w; the caption gives r, θ and the sideways shift, or the time T/2.
d (diagram) -- the diagramq (number) -- the chargem (number) -- the massv (number) -- the speedB (number) -- the fieldw (number) -- the strip's widthfield ("in" or "out") -- B through the page: "out" (⊙, +z) or "in" (⊗, -z); out unless givenA charge with v at θ to B: the field lines along the axis, the projected helix (three turns) with r and the pitch marked, the v arrow and θ, the caption r, pitch and T.
d (diagram) -- the diagramq (number) -- the chargem (number) -- the massv (number) -- the speedtheta (number) -- the angle between v and B in degreesB (number) -- the fieldCrossed fields between two plates (E down, B into the page): a positive charge at v passes straight when v = E/B, bends towards the + plate when v > E/B (qvB > qE) and towards the - plate when v < E/B; the caption says which.
d (diagram) -- the diagramE (number) -- the electric fieldB (number) -- the magnetic fieldv (number) -- the charge's speedThe two dees either side of the gap, B out of the page, the spiral path by half-turns of radius R sqrt(k/N) joined across the gap, the exit; the captions f = qB/2πm and T, then K_max = q²B²R²/2m in J and eV with v_max.
d (diagram) -- the diagramq (number) -- the chargem (number) -- the massB (number) -- the fieldR (number) -- the dee radiusA straight wire seen end-on: its ⊙ or ⊗ at the centre, concentric circles at d1, 2d1, ... with tangent arrowheads by the right-hand rule (anticlockwise for a current out of the page), d marked, B at the outer ring written; the caption B = μ0 I/2πd at d1.
d (diagram) -- the diagramI (number) -- the currentcurrent ("in" or "out") -- the current through the paged1 (number) -- the first ring's radius (0.01 m unless given)rings (number) -- the number of rings, 1 to 8 (3 unless given)The Biot-Savart element: a long wire with its current, the element dl at x, the point P at perpendicular distance d, the vector r, the angle θ between dl and r, the dB mark at P (out of the page for a current along +x and P above); the caption dB/dl = μ0 I sinθ/4πr².
d (diagram) -- the diagramI (number) -- the currentd (number) -- P's perpendicular distance from the wirex (number) -- the element's position along the wire from the foot of PA planar wire shape (the parts as `wireShapeField` takes them, or from `polygonWire`) drawn with current arrowheads, and the field at O (or at the point P given by x, y) as a ⊙ or ⊗ with its value in the caption: the arcs plus straight segments, squares, hexagons and loops with leads of the JEE Biot-Savart figures.
d (diagram) -- the diagramI (number) -- the currentparts (list) -- the arcs and segments in the current's orderx (number) -- optional: the point's xy (number) -- optional: the point's yTwo long parallel wires d apart with their currents (up for positive), the field of each at the other as a ⊙ or ⊗, the force arrows (towards each other for like currents), d marked; the caption F/L = μ0 I1 I2/2πd and F on L.
d (diagram) -- the diagramI1 (number) -- the left wire's currentI2 (number) -- the right wire'sd (number) -- the separationL (number) -- the length the force is given for (1 m unless given)A straight conductor in a uniform field. With B through the page (the default, or "in"/"out" as the mode): the field marks, the wire along x with its current, the force arrow in the plane by F = I L × B. With the mode "plane" (the default when θ is given): B along +x as lines, the wire at θ to it, the force through the page as a mark. The caption F = BIL sinθ.
d (diagram) -- the diagramI (number) -- the currentL (number) -- the lengthB (number) -- the fieldtheta (number) -- the angle between the conductor and B in degrees (90 unless given)mode ("in", "out" or "plane") -- where B pointsA coil edge-on in a uniform field along +x, its normal at θ to B: the field lines, the coil as a thick segment with ⊙ and ⊗ at its ends for the current's sense, the m (or n) arrow, the angle arc; with "torque" (the default) the force couple on the ends and the caption m = NIA, τ = mB sinθ, U = -mB cosθ; with "flux" the caption Φ = NBA cosθ.
d (diagram) -- the diagramN (number) -- the turnsI (number) -- the currentA (number) -- the area (the coil is drawn sqrt(A) long)B (number) -- the fieldtheta (number) -- the angle between the normal and B in degreesmode ("torque" or "flux") -- what the caption givesA rod of length l sliding at v on rails closed by R in a field through the page: the rails, the resistor, the rod, the field marks, the v arrow, the induced current's sense by Lenz's law (arrowheads on the rod and the rails), the retarding force; the caption emf = Blv, I, F = BIl, P = I²R.
d (diagram) -- the diagramB (number) -- the fieldl (number) -- the rod's length (the rails' spacing)v (number) -- the speed (negative to the left)R (number) -- the resistancefield ("in" or "out") -- B through the page: "out" (⊙, +z) or "in" (⊗, -z); out unless givenA rod turning about one end in a field through the page: the field marks, the dashed circle it sweeps, the rod OP, the ω arc, the + and - ends by the right-hand rule; the caption emf = Bωl²/2.
d (diagram) -- the diagramB (number) -- the fieldl (number) -- the rod's lengthomega (number) -- the angular speed in rad/s (positive anticlockwise)field ("in" or "out") -- B through the page: "out" (⊙, +z) or "in" (⊗, -z); out unless givenA rectangular loop moving at v across a strip of field through the page (the strip from x = 0 to x = strip), its leading edge at x: the field marks, the loop with the part inside shaded, the v arrow, the induced current's sense while entering or leaving (none while fully inside); the caption gives the state, Φ and the emf, as `loopRegionEmf` does.
d (diagram) -- the diagramstrip (number) -- the strip's widthw (number) -- the loop's widthh (number) -- its heightB (number) -- the fieldv (number) -- the speedx (number) -- the leading edge's positionfield ("in" or "out") -- B through the page: "out" (⊙, +z) or "in" (⊗, -z); out unless givenThe field lines of a circular current loop seen edge-on (its two cuts as ⊙ and ⊗), traced from the ring's Biot-Savart field with the engine's RK4 from seeds across the loop, arrowheads along the field, O marked; the caption B at the centre = μ0 I/2R. The lines are closed curves: along the axis inside, round the wire outside.
d (diagram) -- the diagramR (number) -- the radiusI (number) -- the current (positive: the field inside along +x)lines (number) -- the number of lines, 1 to 16 (8 unless given)A solenoid in section: its turns as ⊙ above and ⊗ below (at most 40 drawn, carrying the whole current), the traced field lines (uniform inside, returning outside), the caption B = μ0 n I.
d (diagram) -- the diagramn (number) -- the turns per metreI (number) -- the currentlength (number) -- the solenoid's lengthradius (number) -- its radiuslines (number) -- the number of lines, 1 to 16 (8 unless given)A toroid seen from above: the core between r1 and r2, the winding marks on its two edges, dashed circular field lines inside with their sense, r marked, B = 0 written in the hole; the caption B = μ0 N I/2πr at the mean radius.
d (diagram) -- the diagramN (number) -- the total turnsI (number) -- the currentr1 (number) -- the inner radiusr2 (number) -- the outer radiusA bar magnet with its field lines: the S and N halves coloured, the lines traced from the equivalent solenoid's field (S to N inside, N round to S outside, closed curves) with arrowheads.
d (diagram) -- the diagramlength (number) -- the magnet's lengthwidth (number) -- its widthlines (number) -- the number of lines, 1 to 16 (8 unless given)Lenz's law: a bar magnet with the named pole facing a coil, moving towards it or away, the coil edge-on with its turns' ⊙ and ⊗ in the sense the law gives, the faces' induced poles written, and a front view of the current seen from the magnet; the caption explains (a pole approaching is repelled: the near face becomes the same pole).
d (diagram) -- the diagrampole ("N" or "S") -- the pole facing the coilmotion ("towards" or "away") -- the magnet's motionturns (number) -- the turns drawn, 1 to 12 (4 unless given)