{-# OPTIONS_GHC -Wall #-} {-# LANGUAGE Trustworthy #-} {- | Module : Physics.Learn.Current Copyright : (c) Scott N. Walck 2012-2014 License : BSD3 (see LICENSE) Maintainer : Scott N. Walck Stability : experimental This module contains functions for working with current, magnetic field, and magnetic flux. -} module Physics.Learn.Current ( -- * Current Current , CurrentDistribution(..) -- * Magnetic Field , bField , bFieldFromLineCurrent , bFieldFromSurfaceCurrent , bFieldFromVolumeCurrent -- * Magnetic Flux , magneticFlux ) where import Physics.Learn.CarrotVec ( magnitude , (*^) , (^/) , (><) ) import Physics.Learn.Position ( VectorField , displacement , addFields ) import Physics.Learn.Curve ( Curve(..) , crossedLineIntegral ) import Physics.Learn.Surface ( Surface(..) , surfaceIntegral , dottedSurfaceIntegral ) import Physics.Learn.Volume ( Volume(..) , volumeIntegral ) -- | Electric current, in units of Amperes (A) type Current = Double -- | A current distribution is a line current (current through a wire), a surface current, -- a volume current, or a combination of these. -- The 'VectorField' describes a surface current density -- or a volume current density. data CurrentDistribution = LineCurrent Current Curve -- ^ current through a wire | SurfaceCurrent VectorField Surface -- ^ 'VectorField' is surface current density (A/m) | VolumeCurrent VectorField Volume -- ^ 'VectorField' is volume current density (A/m^2) | MultipleCurrents [CurrentDistribution] -- ^ combination of current distributions -- | Magnetic field produced by a line current (current through a wire). -- The function 'bField' calls this function -- to evaluate the magnetic field produced by a line current. bFieldFromLineCurrent :: Current -- ^ current (in Amps) -> Curve -- ^ geometry of the line current -> VectorField -- ^ magnetic field (in Tesla) bFieldFromLineCurrent i c r = k *^ crossedLineIntegral 1000 integrand c where k = 1e-7 -- mu0 / (4 * pi) integrand r' = (-i) *^ d ^/ magnitude d ** 3 where d = displacement r' r -- | Magnetic field produced by a surface current. -- The function 'bField' calls this function -- to evaluate the magnetic field produced by a surface current. -- This function assumes that surface current density -- will be specified parallel to the surface, and does -- not check if that is true. bFieldFromSurfaceCurrent :: VectorField -- ^ surface current density -> Surface -- ^ geometry of the surface current -> VectorField -- ^ magnetic field (in T) bFieldFromSurfaceCurrent kCurrent c r = k *^ surfaceIntegral 100 100 integrand c where k = 1e-7 -- mu0 / (4 * pi) integrand r' = (kCurrent r' >< d) ^/ magnitude d ** 3 where d = displacement r' r -- | Magnetic field produced by a volume current. -- The function 'bField' calls this function -- to evaluate the magnetic field produced by a volume current. bFieldFromVolumeCurrent :: VectorField -- ^ volume current density -> Volume -- ^ geometry of the volume current -> VectorField -- ^ magnetic field (in T) bFieldFromVolumeCurrent j c r = k *^ volumeIntegral 50 50 50 integrand c where k = 1e-7 -- mu0 / (4 * pi) integrand r' = (j r' >< d) ^/ magnitude d ** 3 where d = displacement r' r -- | The magnetic field produced by a current distribution. -- This is the simplest way to find the magnetic field, because it -- works for any current distribution (line, surface, volume, or combination). bField :: CurrentDistribution -> VectorField bField (LineCurrent i c) = bFieldFromLineCurrent i c bField (SurfaceCurrent kC s) = bFieldFromSurfaceCurrent kC s bField (VolumeCurrent j v) = bFieldFromVolumeCurrent j v bField (MultipleCurrents cds) = addFields \$ map bField cds ------------------- -- Magnetic Flux -- ------------------- -- | The magnetic flux through a surface produced by a current distribution. magneticFlux :: Surface -> CurrentDistribution -> Double magneticFlux surf dist = dottedSurfaceIntegral 100 100 (bField dist) surf