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A point in space for the electrostatics functions. Coordinates are metres, or quantities of length. With one argument, position(t) is the turtle's position instead.
x (number or quantity) -- x coordinatey (number or quantity) -- y coordinatez (number or quantity) -- z coordinateA point charge at a position. Read it with c.x, c.y, c.z and c.q.
position (record) -- Where the charge is, from position()q (number or quantity) -- The charge, in C or as a quantitySeveral point charges as one model, for the field, potential and energy functions.
charges... (record) -- Any number of point chargesThe potential at a point due to a collection of point charges, V = sum of k q / r, zero at infinity. The result is a quantity in volts.
charges (record) -- A charge collectionat (record) -- The point, from position()k (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe electric field at a point due to a collection of point charges, by superposition. The result has .x, .y, .z (N/C) and .units.
charges (record) -- A charge collectionat (record) -- The point, away from every chargek (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe force on a charge in a field, F = q E. The result has .x, .y, .z in newtons.
q (number or quantity) -- The chargefield (record) -- A field, as electricFieldAt gives itThe potential of a collection of point charges as a formula in x, y and z.
charges (record) -- A charge collectionk (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe electric field of a collection of point charges as formulas in x, y and z: E = -grad V, worked symbolically. Read the components with E.x, E.y, E.z.
charges (record) -- A charge collectionk (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe electrostatic energy of a collection of point charges: the sum of k q1 q2 / r over every pair. The result is a quantity in joules.
charges (record) -- A charge collectionk (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe work done by the field of a collection of charges on a test charge moved from one point to another, W = q (V_from - V_to). The result is a quantity in joules.
q (number or quantity) -- The test chargecharges (record) -- The charges making the fieldfrom (record) -- Starting pointto (record) -- End pointk (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe dipole moment of a collection of charges about a point, p = sum of q r. The result has .x, .y, .z in C m.
charges (record) -- A charge collectionorigin (record) -- Optional reference point; the origin when left outThe torque on a dipole in a uniform field, the cross product p x E. The result has .x, .y, .z in N m.
p (record or vector) -- Dipole moment, in C mE (record or vector) -- Field, in N/CThe energy of a dipole in a uniform field, U = -p . E. The result is a quantity in joules.
p (record or vector) -- Dipole moment, in C mE (record or vector) -- Field, in N/CThe electric flux through a closed surface around a charge, by Gauss's law: Q / eps0. The result is a quantity in N m^2/C.
Q (number or quantity) -- Enclosed chargeThe field at a distance from a spherically symmetric charge, by Gauss's law: Q / (4 pi eps0 r^2). The result is a quantity in N/C.
Q (number or quantity) -- Enclosed charger (number or quantity) -- Distance from the centreThe field at a distance from a long straight line of charge: lambda / (2 pi eps0 r). The result is a quantity in N/C.
lambda (number or quantity) -- Charge per unit length, C/mr (number or quantity) -- Distance from the lineThe field of a large flat sheet of charge: sigma / (2 eps0), the same at every distance. The result is a quantity in N/C.
sigma (number or quantity) -- Charge per unit area, C/m^2The potential of a thin charged spherical shell: k Q / R everywhere inside, k Q / r outside. The result is a quantity in volts.
Q (number or quantity) -- Total charge, in C or as a quantityR (number or quantity) -- Radius of the shell or spherer (number or quantity) -- Distance of the point from the centrek (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe radial field of a thin charged spherical shell: zero inside, k Q / r^2 outside. The result is a quantity in N/C.
Q (number or quantity) -- Total charge, in C or as a quantityR (number or quantity) -- Radius of the shell or spherer (number or quantity) -- Distance of the point from the centrek (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe potential of a uniformly charged solid sphere: k Q (3 R^2 - r^2) / (2 R^3) inside, k Q / r outside. The result is a quantity in volts.
Q (number or quantity) -- Total charge, in C or as a quantityR (number or quantity) -- Radius of the shell or spherer (number or quantity) -- Distance of the point from the centrek (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe radial field of a uniformly charged solid sphere: k Q r / R^3 inside, k Q / r^2 outside. The result is a quantity in N/C.
Q (number or quantity) -- Total charge, in C or as a quantityR (number or quantity) -- Radius of the shell or spherer (number or quantity) -- Distance of the point from the centrek (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe potential on the axis of a uniformly charged ring: k Q / sqrt(R^2 + z^2). The result is a quantity in volts.
Q (number or quantity) -- Total charge, in C or as a quantityR (number or quantity) -- Radius of the ring, which lies in the xy planez (number or quantity) -- Signed distance along the axisk (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe field along the axis of a uniformly charged ring: k Q z / (R^2 + z^2)^(3/2). The result is a quantity in N/C.
Q (number or quantity) -- Total charge, in C or as a quantityR (number or quantity) -- Radius of the ring, which lies in the xy planez (number or quantity) -- Signed distance along the axisk (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe potential on the line of a uniformly charged rod, beyond its end. It contains a logarithm, so the value is approximate. The result is a quantity in volts.
Q (number or quantity) -- Total charge, in C or as a quantityL (number or quantity) -- Length of the rod, which lies along the x axis centred at the originx (number or quantity) -- Position on the x axis, beyond the end of the rodk (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe field on the line of a uniformly charged rod, beyond its end: k (Q/L) (1/|x - L/2| - 1/|x + L/2|). The result is a quantity in N/C.
Q (number or quantity) -- Total charge, in C or as a quantityL (number or quantity) -- Length of the rod, which lies along the x axis centred at the originx (number or quantity) -- Position on the x axis, beyond the end of the rodk (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe potential on the perpendicular bisector of a uniformly charged rod. It contains an inverse hyperbolic sine, so the value is approximate. The result is a quantity in volts.
Q (number or quantity) -- Total charge, in C or as a quantityL (number or quantity) -- Length of the rod, which lies along the x axis centred at the originy (number or quantity) -- Distance from the rod along its perpendicular bisector, not zerok (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe field on the perpendicular bisector of a uniformly charged rod: k Q / (y sqrt(y^2 + (L/2)^2)). The result is a quantity in N/C.
Q (number or quantity) -- Total charge, in C or as a quantityL (number or quantity) -- Length of the rod, which lies along the x axis centred at the originy (number or quantity) -- Distance from the rod along its perpendicular bisector, not zerok (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe potential on the axis of a uniformly charged disk: sigma (sqrt(R^2 + z^2) - |z|) / (2 eps0). The result is a quantity in volts.
sigma (number or quantity) -- Charge per unit area, C/m^2R (number or quantity) -- Radius of the disk, which lies in the xy planez (number or quantity) -- Signed distance along the axisThe field along the axis of a uniformly charged disk: sigma (1 - |z| / sqrt(R^2 + z^2)) / (2 eps0), pointing away from a positive disk. The result is a quantity in N/C.
sigma (number or quantity) -- Charge per unit area, C/m^2R (number or quantity) -- Radius of the disk, which lies in the xy planez (number or quantity) -- Signed distance along the axisThe potential at distance r from a long line of charge, measured from a reference distance r0: V(r) - V(r0) = -lambda ln(r / r0) / (2 pi eps0). Approximate (a logarithm). The result is a quantity in volts.
lambda (number or quantity) -- Charge per unit length, C/mr (number or quantity) -- Distance of the point from the liner0 (number or quantity) -- Reference distance, where the potential is taken as zeroThe potential at distance z from a large flat sheet of charge, measured from a reference distance z0: V(z) - V(z0) = -sigma (|z| - |z0|) / (2 eps0). The result is a quantity in volts.
sigma (number or quantity) -- Charge per unit area, C/m^2z (number or quantity) -- Distance of the point from the sheetz0 (number or quantity) -- Reference distanceThe radial field of a long uniformly charged solid cylinder: lambda r / (2 pi eps0 R^2) inside, lambda / (2 pi eps0 r) outside. The result is a quantity in N/C.
lambda (number or quantity) -- Charge per unit length of the cylinder, C/mR (number or quantity) -- Radius of the cylinderr (number or quantity) -- Distance of the point from the axisThe potential of a long uniformly charged solid cylinder, measured from its surface (V = 0 at r = R). The result is a quantity in volts.
lambda (number or quantity) -- Charge per unit length of the cylinder, C/mR (number or quantity) -- Radius of the cylinderr (number or quantity) -- Distance of the point from the axisThe radial field of a long thin charged cylindrical shell: zero inside, lambda / (2 pi eps0 r) outside. The result is a quantity in N/C.
lambda (number or quantity) -- Charge per unit length of the cylinder, C/mR (number or quantity) -- Radius of the cylinderr (number or quantity) -- Distance of the point from the axisThe potential of a long thin charged cylindrical shell, measured from its surface: zero inside, -lambda ln(r / R) / (2 pi eps0) outside. The result is a quantity in volts.
lambda (number or quantity) -- Charge per unit length of the cylinder, C/mR (number or quantity) -- Radius of the cylinderr (number or quantity) -- Distance of the point from the axisThe capacitance of two parallel plates, eps A / d, ignoring the fringe field. The result is a quantity in farads.
A (number or quantity) -- Plate area, m^2d (number or quantity) -- Gap between the plateseps (number) -- Optional absolute permittivity in F/m; the vacuum's when left out (eps = 1 gives an exact classroom model)The capacitance with a dielectric filling the gap: kappa times the vacuum capacitance. The result is a quantity in farads.
C0 (number or quantity) -- Capacitance without the dielectrickappa (number) -- Relative permittivity (dielectric constant)The charge on a capacitor, Q = C V. The result is a quantity in coulombs.
C (number or quantity) -- CapacitanceV (number or quantity) -- Voltage across itThe voltage across a capacitor, V = Q / C. The result is a quantity in volts.
Q (number or quantity) -- ChargeC (number or quantity) -- CapacitanceThe energy stored in a capacitor, U = Q^2 / (2 C). The result is a quantity in joules.
Q (number or quantity) -- ChargeC (number or quantity) -- CapacitanceCapacitors in series: 1 / C = 1 / C1 + 1 / C2 + ... The result is a quantity in farads.
C1, C2, ... (number or quantity) -- The capacitancesCapacitors in parallel: C = C1 + C2 + ... The result is a quantity in farads.
C1, C2, ... (number or quantity) -- The capacitancesA capacitor that stays connected to its battery while a dielectric is put in: the voltage is fixed, the charge and energy rise. The result has .capacitance, .charge, .voltage and .energy, each a quantity.
C0 (number or quantity) -- Capacitance beforeV (number or quantity) -- Battery voltagekappa (number) -- Relative permittivity of the dielectricA charged capacitor that is disconnected before a dielectric is put in: the charge is fixed, the voltage and energy fall. The result has .capacitance, .charge, .voltage and .energy, each a quantity.
C0 (number or quantity) -- Capacitance beforeQ (number or quantity) -- Charge on the plateskappa (number) -- Relative permittivity of the dielectricThe energy per unit volume of an electric field, u = eps E^2 / 2. The result is a quantity in J/m^3.
eps (number or quantity) -- Absolute permittivity, F/mE (number or quantity) -- Field strength, N/CThe capacitance of a conducting sphere on its own, R / k = 4 pi eps0 R. The result is a quantity in farads.
R (number or quantity) -- Radius of the spherek (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe capacitance of two concentric conducting spheres, a b / (k (b - a)). The result is a quantity in farads.
a (number or quantity) -- Inner radiusb (number or quantity) -- Outer radius, larger than aThe charges on two distant conducting spheres after they are joined by a thin wire: the total charge is shared in proportion to the radii. The result has .first and .second, each a quantity in coulombs.
R1 (number or quantity) -- Radius of the first sphereR2 (number or quantity) -- Radius of the second sphereQ1 (number or quantity) -- Charge on the first before joiningQ2 (number or quantity) -- Charge on the second before joiningThe potential of a point dipole, V = k (p . r) / r^3. The result is a quantity in volts.
p (record or vector) -- Dipole moment, in C mr (record) -- The point, measured from the dipole, from position()k (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelThe field of a point dipole, E = k (3 (p . r) r / r^5 - p / r^3). The result has .x, .y, .z in N/C.
p (record or vector) -- Dipole moment, in C mr (record) -- The point, measured from the dipole, from position()k (number) -- Optional Coulomb constant in N m^2/C^2. Left out, the physical constant is used and the result is approximate (it contains pi); k = 1 gives an exact classroom modelA parallel-plate capacitor with a dielectric covering a fraction of the plate area (the two parts act in parallel): C0 (1 - f + kappa f). The result is a quantity in farads.
C0 (number or quantity) -- Capacitance without the dielectrickappa (number) -- Relative permittivityf (number) -- Fraction of the plate area covered, from 0 to 1A parallel-plate capacitor with a dielectric slab thinner than the gap (the slab and the remaining gap act in series): eps A / (d - t + t / kappa). The result is a quantity in farads.
A (number or quantity) -- Plate area, m^2d (number or quantity) -- Gap between the platest (number or quantity) -- Thickness of the slab, at most dkappa (number) -- Relative permittivity of the slabeps (number) -- Optional absolute permittivity in F/m; the vacuum's when left out (eps = 1 gives an exact classroom model)The capacitance of a long coaxial pair of cylinders, 2 pi eps L / ln(b / a), ignoring the ends. Approximate (a logarithm). The result is a quantity in farads.
a (number or quantity) -- Inner radiusb (number or quantity) -- Outer radius, larger than aL (number or quantity) -- Lengtheps (number) -- Optional absolute permittivity in F/m; the vacuum's when left out (eps = 1 gives an exact classroom model)