EF_dipole.py

from mpmath import mp
from math import cos, radians

# * Initializing accuracy level and value of const_k
mp.dps = 100
const_k = mp.fmul(8.9875518, 10**9)

def dipole_moment(charge, a):

    # Editing Value of charge as per the unit
    print(type(charge), type(a))

    if charge[1] in ('Coulomb', 'C'):
        charge = charge[0]
    elif charge[1] in ('microCoulomb', 'uC'):
        charge = mp.fmul(charge[0], 10**(-6) )
    elif charge[1] in ('milliCoulomb', 'mC'):
        charge = mp.fmul(charge[0], 10**(-3) )
    elif charge[1] in ('electronCharge', 'eC'):
        charge = mp.fmul(charge[0], mp.fmul(1.60217646, mp.fmul(10, -19) ) )                                             # 1.60217646⋅10-19
    elif charge[1] in ('nanoCoulomb', 'nC'):
        charge = mp.fmul(charge[0], mp.power(10, -10) )
    elif charge[1] in ('picoCoulomb', 'pC'):
        charge = mp.fmul( charge[0], mp.power(10, -12) )

    # Editing value of a as per the unit
    if a[1].lower() in ('meters', 'm'):
        a = a[0]
    elif a[1].lower() in ('centimeters', 'cm'):
        a = mp.fmul(a[0], 10**(-2) )
    elif a[1].lower() in ('millimeters', 'mm'):
        a = mp.fmul(a[0], 10**(-3) )
    elif a[1].lower() in ('angstroms', 'a', 'A'):
        a = mp.fmul(a[0], 10**(-10) )

    return mp.fmul(charge, mp.fmul(2, a))


def dipole(r, theta, charge, a):
    '''
    Purpose      : To calculate Electric Potential due to Dipole considering very small values

    Formula Used :

            (q/const_k)*(1/r_1 - 1/r_2)

                   where,
                        r_1     = distance between negative charge and point of observation
                                = (r^2 + a^2 - 2*a*Cos(theta))^0.5
                        r_2     = distance between positive charge and point of observation
                                = (r^2 + a^2 + 2*a*Cos(theta))^0.5
                        const_k = 4*pi*epsilon_not
                                = 8.9875518 x 10^9

    Parameters   :
                   a) r      - distance between center of the dipole and point of observation
                   b) theta  - Angle between positive charge and point of observation
                   c) charge - either charge irrespective of sign
                   d) a      - distance between either charge and center of dipole
    '''



    '''
    Editing Values of the arguments as per the values received by this function
    '''

    print('Values Received by dipole function')
    print(r,a,theta,charge)

    # Editing value of r as per the unit
    if r[1].lower() in ('meters', 'm'):
        r = r[0]
    elif r[1].lower() in ('centimeters', 'cm'):
        r = mp.fmul(r[0], 10**(-2) )
    elif r[1].lower() in ('millimeters', 'mm'):
        r = mp.fmul(r[0], 10**(-3) )
    elif r[1].lower() in ('angstroms', 'a', 'A'):
        r = mp.fmul(r[0], 10**(-10) )

    # Editing value of a as per the unit
    if a[1].lower() in ('meters', 'm'):
        a = a[0]
    elif a[1].lower() in ('centimeters', 'cm'):
        a = mp.fmul(a[0], 10**(-2) )
    elif a[1].lower() in ('millimeters', 'mm'):
        a = mp.fmul(a[0], 10**(-3) )
    elif a[1].lower() in ('angstroms', 'a', 'A'):
        a = mp.fmul(a[0], 10**(-10) )

    # Calculating Value of Cos(theta)
    if theta[1].lower() == 'radians':
        cos_theta = round( cos(theta[0]), 5 )
    elif theta[1].lower() == 'degrees':
        cos_theta = round( mp.cos(mp.radians(theta[0])), 5 )

    # Editing Value of charge as per the unit
    if charge[1] in ('Coulomb', 'C'):
        charge = charge[0]
    elif charge[1] in ('microCoulomb', 'uC'):
        charge = mp.fmul(charge[0], 10**(-6) )
    elif charge[1] in ('milliCoulomb', 'mC'):
        charge = mp.fmul(charge[0], 10**(-3) )
    elif charge[1] in ('electronCharge', 'eC'):
        charge = mp.fmul(charge[0], mp.fmul(1.60217646, mp.fmul(10, -19) ) )                                         # 1.60217646⋅10-19
    elif charge[1] in ('nanoCoulomb', 'nC'):
        charge = mp.fmul(charge[0], mp.power(10, -10) )
    elif charge[1] in ('picoCharge', 'pC'):
        charge = mp.fmul( charge[0], mp.power(10, -12) )


    theta = round( mp.cos(mp.radians(theta[0])), 5 )
    print('Charge=', charge)
    print('a=', a)
    print('r=', r)
    print('theta=', theta)
    print('cos theta=', cos_theta)


    r_1 = mp.sqrt(mp.fsub(mp.fadd(mp.power(r, 2), mp.power(a, 2)), mp.fmul(2, mp.fmul(a, mp.fmul(r, cos_theta)))))
    r_2 = mp.sqrt(mp.fadd(mp.fadd(mp.power(r, 2), mp.power(a, 2)), mp.fmul(2, mp.fmul(a, mp.fmul(r, cos_theta)))))
    
    # Calculating final result
    result = mp.fmul(mp.fmul(charge, const_k), mp.fsub(mp.fdiv(1, r_1), mp.fdiv(1, r_2)))

    print('exact: ',result)

    # returning final result
    return result


def dipole_approx(r, theta, charge, a):
    '''
    Purpose      : To calculate Electric Potential due to Dipole neglecting very small value of a^2

    Formula Used :
            q*2*a*cos(theta)/( const_k*(r^2) )
                   where,
                    const_k = 4*pi*epsilon_not
                            = 8.9875518 x 10^9

    Parameters   :
                   a) r      - distance between center of the dipole and point of observation
                   b) theta  - Angle between positive charge and point of observation
                   c) charge - either charge irrespective of sign
                   d) a      - distance between either charge and center of dipole
    '''


    '''
    Editing Values of the arguments as per the values received by this function
    '''
    # Editing value of r as per the unit
    if r[1].lower() in ('meters', 'm'):
        r = r[0]
    elif r[1].lower() in ('centimeters', 'cm'):
        r = mp.fmul(r[0], 10**(-2) )
    elif r[1].lower() in ('millimeters', 'mm'):
        r = mp.fmul(r[0], 10**(-3) )
    elif r[1].lower() in ('angstroms', 'a', 'A'):
        r = mp.fmul(r[0], 10**(-10) )

    # Editing value of a as per the unit
    if a[1].lower() in ('meters', 'm'):
        a = a[0]
    elif a[1].lower() in ('centimeters', 'cm'):
        a = mp.fmul(a[0], 10**(-2) )
    elif a[1].lower() in ('millimeters', 'mm'):
        a = mp.fmul(a[0], 10**(-3) )
    elif a[1].lower() in ('angstroms', 'a', 'A'):
        a = mp.fmul(a[0], 10**(-10) )

    # Calculating Value of Cos(theta)
    if theta[1].lower() == 'radians':
        cos_theta = round( cos(theta[0]), 5 )
    elif theta[1].lower() == 'degrees':
        cos_theta = round( cos(mp.radians(theta[0])), 5 )

    # Editing Value of charge as per the unit
    if charge[1] in ('Coulomb', 'C'):
        charge = charge[0]
    elif charge[1] in ('microCoulomb', 'uC'):
        charge = mp.fmul(charge[0], 10**(-6) )
    elif charge[1] in ('milliCoulomb', 'mC'):
        charge = mp.fmul(charge[0], 10**(-3) )
    elif charge[1] in ('electronCharge', 'eC'):
        charge = mp.fmul(charge[0], mp.fmul(1.60217646, mp.fmul(10, -19) ) )                                         # 1.60217646⋅10-19
    elif charge[1] in ('nanoCoulomb', 'nC'):
        charge = mp.fmul(charge[0], mp.power(10, -10) )
    elif charge[1] in ('picoCharge', 'pC'):
        charge = mp.fmul( charge[0], mp.power(10, -12) )

    # Applying Formula to given parameters
    result = mp.fdiv(mp.fmul(const_k, mp.fmul(charge, mp.fmul(2, mp.fmul(a, cos_theta)))), mp.power(r,2))
    print('approx', result)

    # returning final result
    return result


def diff(EP:float, AP:float):
    return mp.fsub(EP, AP)


if __name__ == "__main__":
    print(mp) # Configurations of mpmath

    # Testing Values
    r = (float(1)  , 'meters')    # in meters
    theta = (float(60), 'degrees' )  # in degrees
    charge = (float(1), 'Coulomb')   # in coulombs
    a = (float(1), 'meters') # in meters

    exact  = dipole(r, theta, charge, a) # Exact Electric Potential due to Dipole
    approx = dipole_approx(r, theta, charge, a) # Approx Electric Potential to Dipole

    error = diff(exact, approx) # Error

    # Printing Results
    print('Exact Result  : ', exact)
    print('Approx Result : ', approx)
    print('Difference    : ', error)