charges module

Module contains the abstract base class Charge and example subclasses.

Charge is an abstract base class representing a point charge. The class has abstract methods for the position, velocity, and acceleration of the charge in the x, y, and z directions.

Subclasses, such as OscillatingCharge, define their own time-dependent trajectories. These classes are used by the Simulation class to perform electromagnetism calculations and simulations.

All units are in SI.

Charge

Abstract base class used to define a point charge object.

Subclasses implement their unique position, velocity, and acceleration methods in x, y, and z as functions of time. By default, the velocity and acceleration values are determined using finite difference approximations from the position methods; however, they can also be explicitly specified.

Parameters:

Name	Type	Description	Default
q	float	Charge value, can be positive or negative.	required
h	float	Limit for finite difference calculations for vel and acc.	required

solve_time(self, tr, t, x, y, z)

Return equation to solve for the retarded time of the charge.

Source code in pycharge/charges.py

def solve_time(
    self, tr: ndarray, t: ndarray, x: ndarray, y: ndarray, z: ndarray
) -> ndarray:
    """Return equation to solve for the retarded time of the charge."""
    # Griffiths Eq. 10.55
    return ((x-self.xpos(tr))**2 + (y-self.ypos(tr))**2
            + (z-self.zpos(tr))**2)**0.5 - c*(t-tr)

xacc(self, t)

Return x acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
Union[ndarray, float]	x acceleration at time values.

Source code in pycharge/charges.py

def xacc(self, t: Union[ndarray, float]) -> Union[ndarray, float]:
    """Return x acceleration of the charge at specified array of times.

    Args:
        t: 3D meshgrid array of time values.

    Returns:
        x acceleration at time values.
    """
    return (self.xvel(t+0.5*self.h)-self.xvel(t-0.5*self.h))/self.h

xpos(self, t)

Return x position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
Union[ndarray, float]	x positions at time values.

Source code in pycharge/charges.py

@abstractmethod
def xpos(self, t: Union[ndarray, float]) -> Union[ndarray, float]:
    """Return x position of the charge at specified array of times.

    Args:
        t: 3D meshgrid array of time values.

    Returns:
        x positions at time values.
    """

xvel(self, t)

Return x velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
Union[ndarray, float]	x velocity at time values.

Source code in pycharge/charges.py

def xvel(self, t: Union[ndarray, float]) -> Union[ndarray, float]:
    """Return x velocity of the charge at specified array of times.

    Args:
        t: 3D meshgrid array of time values.

    Returns:
        x velocity at time values.
    """
    return (self.xpos(t+0.5*self.h)-self.xpos(t-0.5*self.h))/self.h

yacc(self, t)

Return y acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
Union[ndarray, float]	y acceleration at time values.

Source code in pycharge/charges.py

def yacc(self, t: Union[ndarray, float]) -> Union[ndarray, float]:
    """Return y acceleration of the charge at specified array of times.

    Args:
        t: 3D meshgrid array of time values.

    Returns:
        y acceleration at time values.
    """
    return (self.yvel(t+0.5*self.h)-self.yvel(t-0.5*self.h))/self.h

ypos(self, t)

Return y position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
Union[ndarray, float]	y position at time values.

Source code in pycharge/charges.py

@abstractmethod
def ypos(self, t: Union[ndarray, float]) -> Union[ndarray, float]:
    """Return y position of the charge at specified array of times.

    Args:
        t: 3D meshgrid array of time values.

    Returns:
        y position at time values.
    """

yvel(self, t)

Return y velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
Union[ndarray, float]	y velocity at time values.

Source code in pycharge/charges.py

def yvel(self, t: Union[ndarray, float]) -> Union[ndarray, float]:
    """Return y velocity of the charge at specified array of times.

    Args:
        t: 3D meshgrid array of time values.

    Returns:
        y velocity at time values.
    """
    return (self.ypos(t+0.5*self.h)-self.ypos(t-0.5*self.h))/self.h

zacc(self, t)

Return z acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
Union[ndarray, float]	z acceleration at time values.

Source code in pycharge/charges.py

def zacc(self, t: Union[ndarray, float]) -> Union[ndarray, float]:
    """Return z acceleration of the charge at specified array of times.

    Args:
        t: 3D meshgrid array of time values.

    Returns:
        z acceleration at time values.
    """
    return (self.zvel(t+0.5*self.h)-self.zvel(t-0.5*self.h))/self.h

zpos(self, t)

Return z position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
Union[ndarray, float]	z position at time values.

Source code in pycharge/charges.py

@abstractmethod
def zpos(self, t: Union[ndarray, float]) -> Union[ndarray, float]:
    """Return z position of the charge at specified array of times.

    Args:
        t: 3D meshgrid array of time values.

    Returns:
        z position at time values.
    """

zvel(self, t)

Return z velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
Union[ndarray, float]	z velocity at time values.

Source code in pycharge/charges.py

def zvel(self, t: Union[ndarray, float]) -> Union[ndarray, float]:
    """Return z velocity of the charge at specified array of times.

    Args:
        t: 3D meshgrid array of time values.

    Returns:
        z velocity at time values.
    """
    return (self.zpos(t+0.5*self.h)-self.zpos(t-0.5*self.h))/self.h

LinearAcceleratingCharge

Linearly accelerating charge along the x-axis.

At t<0, the charge is stationary at the origin (x=0, y=0, z=0) and begins accelerating at t=0. The charge stops accelerating at the time given by stop_t and continues moving at a constant velocity.

Parameters:

Name	Type	Description	Default
acceleration	float	Accleration along x-axis. Positive value is in +x direction, negative is in -x direction.	required
stop_t	Optional[float]	Time when charge stops accelerating. If None, the charge stops accelerating when the velocity reaches 0.999c. Defaults to None.	required
q	float	Charge value, can be positive or negative. Default is e.	required

xacc(self, t)

Return x acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x acceleration at time values.

Source code in pycharge/charges.py

def xacc(self, t: Union[ndarray, float]) -> ndarray:
    t = np.array(t)
    xacc = self.acceleration*np.ones(t.shape)
    xacc[t < 0] = 0
    xacc[t > self.stop_t] = 0
    return xacc

xpos(self, t)

Return x position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x positions at time values.

Source code in pycharge/charges.py

def xpos(self, t: Union[ndarray, float]) -> ndarray:
    t = np.array(t)
    xpos = 0.5*self.acceleration*t**2
    xpos[t < 0] = 0
    xpos[t > self.stop_t] = (
        0.5*self.acceleration*self.stop_t**2
        + self.acceleration*self.stop_t * (t[t > self.stop_t]-self.stop_t)
    )
    return xpos

xvel(self, t)

Return x velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x velocity at time values.

Source code in pycharge/charges.py

def xvel(self, t: Union[ndarray, float]) -> ndarray:
    t = np.array(t)
    xvel = self.acceleration*t
    xvel[t < 0] = 0
    xvel[t > self.stop_t] = self.acceleration*self.stop_t
    return xvel

yacc(self, t)

Return y acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	y acceleration at time values.

Source code in pycharge/charges.py

def yacc(self, t: Union[ndarray, float]) -> float:
    return 0

ypos(self, t)

Return y position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	y position at time values.

Source code in pycharge/charges.py

def ypos(self, t: Union[ndarray, float]) -> float:
    return 0

yvel(self, t)

Return y velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	y velocity at time values.

Source code in pycharge/charges.py

def yvel(self, t: Union[ndarray, float]) -> float:
    return 0

zacc(self, t)

Return z acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z acceleration at time values.

Source code in pycharge/charges.py

def zacc(self, t: Union[ndarray, float]) -> float:
    return 0

zpos(self, t)

Return z position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z position at time values.

Source code in pycharge/charges.py

def zpos(self, t: Union[ndarray, float]) -> float:
    return 0

zvel(self, t)

Return z velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z velocity at time values.

Source code in pycharge/charges.py

def zvel(self, t: Union[ndarray, float]) -> float:
    return 0

LinearDeceleratingCharge

Linearly decelerating charge along the x-axis.

At t<0, the charge is moving at the value of initial_speed. At t=0, the charge is at the origin (x=0, y=0, z=0) and decelerates until the time given by stop_t and continues moving at a constant velocity.

Parameters:

Name	Type	Description	Default
deceleration	float	Deceleration along x-axis. Positive value is in +x direction, negative is in -x direction.	required
initial_speed	float	Initial speed of charge at t<0 along x-axis.	required
stop_t	Optional[float]	Time when the charge stops decelerating. If None, the charge stops decelerating when velocity reaches zero. Defaults to None.	required
q	float	Charge value, can be positive or negative. Default is e.	required

xacc(self, t)

Return x acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x acceleration at time values.

Source code in pycharge/charges.py

def xacc(self, t: Union[ndarray, float]) -> ndarray:
    t = np.array(t)
    xacc = np.zeros(t.shape)
    xacc[t > 0] = -self.deceleration
    xacc[t > self.stop_t] = 0
    return xacc

xpos(self, t)

Return x position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x positions at time values.

Source code in pycharge/charges.py

def xpos(self, t: Union[ndarray, float]) -> ndarray:
    t = np.array(t)
    xpos = self.initial_speed*t
    xpos[t > 0] = (self.initial_speed*t[t > 0]
                   - 0.5*self.deceleration*t[t > 0]**2)
    xpos[t > self.stop_t] = (self.initial_speed * self.stop_t
                             - 0.5*self.deceleration*self.stop_t**2)
    return xpos

xvel(self, t)

Return x velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x velocity at time values.

Source code in pycharge/charges.py

def xvel(self, t: Union[ndarray, float]) -> ndarray:
    t = np.array(t)
    xvel = self.initial_speed*np.ones(t.shape)
    xvel[t > 0] = self.initial_speed - self.deceleration*t[t > 0]
    xvel[t > self.stop_t] = (self.initial_speed
                             - self.deceleration*self.stop_t)
    return xvel

yacc(self, t)

Return y acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	y acceleration at time values.

Source code in pycharge/charges.py

def yacc(self, t: Union[ndarray, float]) -> float:
    return 0

ypos(self, t)

Return y position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	y position at time values.

Source code in pycharge/charges.py

def ypos(self, t: Union[ndarray, float]) -> float:
    return 0

yvel(self, t)

Return y velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	y velocity at time values.

Source code in pycharge/charges.py

def yvel(self, t: Union[ndarray, float]) -> float:
    return 0

zacc(self, t)

Return z acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z acceleration at time values.

Source code in pycharge/charges.py

def zacc(self, t: Union[ndarray, float]) -> float:
    return 0

zpos(self, t)

Return z position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z position at time values.

Source code in pycharge/charges.py

def zpos(self, t: Union[ndarray, float]) -> float:
    return 0

zvel(self, t)

Return z velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z velocity at time values.

Source code in pycharge/charges.py

def zvel(self, t: Union[ndarray, float]) -> float:
    return 0

LinearVelocityCharge

Charge moving with constant velocity along the x-axis.

At t=0, the charge is at the position given by init_pos with the magnitude of the velocity given by speed.

Parameters:

Name	Type	Description	Default
speed	float	Speed of the charge along the x-axis. Positive value is in +x direction, negative is in -x direction.	required
init_pos	float	Initial x position at t=0.	required
q	float	Charge value, can be positive or negative. Default is e.	required

xacc(self, t)

Return x acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	x acceleration at time values.

Source code in pycharge/charges.py

def xacc(self, t: Union[ndarray, float]) -> float:
    return 0

xpos(self, t)

Return x position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x positions at time values.

Source code in pycharge/charges.py

def xpos(self, t: Union[ndarray, float]) -> ndarray:
    t = np.array(t)
    return self.speed*t + self.init_pos

xvel(self, t)

Return x velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	x velocity at time values.

Source code in pycharge/charges.py

def xvel(self, t: Union[ndarray, float]) -> float:
    return self.speed

yacc(self, t)

Return y acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	y acceleration at time values.

Source code in pycharge/charges.py

def yacc(self, t: Union[ndarray, float]) -> float:
    return 0

ypos(self, t)

Return y position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	y position at time values.

Source code in pycharge/charges.py

def ypos(self, t: Union[ndarray, float]) -> float:
    return 0

yvel(self, t)

Return y velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	y velocity at time values.

Source code in pycharge/charges.py

def yvel(self, t: Union[ndarray, float]) -> float:
    return 0

zacc(self, t)

Return z acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z acceleration at time values.

Source code in pycharge/charges.py

def zacc(self, t: Union[ndarray, float]) -> float:
    return 0

zpos(self, t)

Return z position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z position at time values.

Source code in pycharge/charges.py

def zpos(self, t: Union[ndarray, float]) -> float:
    return 0

zvel(self, t)

Return z velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z velocity at time values.

Source code in pycharge/charges.py

def zvel(self, t: Union[ndarray, float]) -> float:
    return 0

OrbittingCharge

Radially orbitting charge in the x-y plane.

At t=0, the charge is at the position (x=radius, y=0, z=0) and orbits counter-clockwise.

Parameters:

Name	Type	Description	Default
radius	float	Radius of the orbitting charge trajectory.	required
omega	float	Angular frequency of the orbit (units: rad/s).	required
start_zero	bool	Determines if the charge begins orbitting at t=0. Defaults to False.	required
stop_t	Optional[float]	Time when the charge stops orbitting. If None, the charge never stops orbitting. Defaults to None.	required
q	float	Charge value, can be positive or negative. Default is e.	required

xacc(self, t)

Return x acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x acceleration at time values.

Source code in pycharge/charges.py

def xacc(self, t: Union[ndarray, float]) -> ndarray:
    xacc = -self.radius*self.omega**2*np.cos(self.omega*t)
    if self.start_zero:
        xacc[t < 0] = 0
    if self.stop_t is not None:
        xacc[t > self.stop_t] = 0
    return xacc

xpos(self, t)

Return x position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x positions at time values.

Source code in pycharge/charges.py

def xpos(self, t: Union[ndarray, float]) -> ndarray:
    xpos = self.radius*np.cos(self.omega*t)
    if self.start_zero:
        xpos[t < 0] = self.radius
    if self.stop_t is not None:
        xpos[t > self.stop_t] = (self.radius
                                 * np.cos(self.omega*self.stop_t))
    return xpos

xvel(self, t)

Return x velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x velocity at time values.

Source code in pycharge/charges.py

def xvel(self, t: Union[ndarray, float]) -> ndarray:
    xvel = -self.radius*self.omega*np.sin(self.omega*t)
    if self.start_zero:
        xvel[t < 0] = 0
    if self.stop_t is not None:
        xvel[t > self.stop_t] = 0
    return xvel

yacc(self, t)

Return y acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	y acceleration at time values.

Source code in pycharge/charges.py

def yacc(self, t: Union[ndarray, float]) -> ndarray:
    yacc = -self.radius*self.omega**2*np.sin(self.omega*t)
    if self.start_zero:
        yacc[t < 0] = 0
    if self.stop_t is not None:
        yacc[t > self.stop_t] = 0
    return yacc

ypos(self, t)

Return y position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	y position at time values.

Source code in pycharge/charges.py

def ypos(self, t: Union[ndarray, float]) -> ndarray:
    ypos = self.radius*np.sin(self.omega*t)
    if self.start_zero:
        ypos[t < 0] = 0
    if self.stop_t is not None:
        ypos[t > self.stop_t] = (self.radius
                                 * np.sin(self.omega*self.stop_t))
    return ypos

yvel(self, t)

Return y velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	y velocity at time values.

Source code in pycharge/charges.py

def yvel(self, t: Union[ndarray, float]) -> ndarray:
    yvel = self.radius*self.omega*np.cos(self.omega*t)
    if self.start_zero:
        yvel[t < 0] = 0
    if self.stop_t is not None:
        yvel[t > self.stop_t] = 0
    return yvel

zacc(self, t)

Return z acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z acceleration at time values.

Source code in pycharge/charges.py

def zacc(self, t: Union[ndarray, float]) -> float:
    return 0

zpos(self, t)

Return z position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z position at time values.

Source code in pycharge/charges.py

def zpos(self, t: Union[ndarray, float]) -> float:
    return 0

zvel(self, t)

Return z velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z velocity at time values.

Source code in pycharge/charges.py

def zvel(self, t: Union[ndarray, float]) -> float:
    return 0

OscillatingCharge

Sinusoidally oscillating charge along a specified axis.

Parameters:

Name	Type	Description	Default
origin	Tuple[float, float, float]	List of x, y, and z values for the oscillating charge's origin.	required
direction	Tuple[float, float, float]	List of x, y, and z values for the charge direction vector.	required
amplitude	float	Amplitude of the oscillations.	required
omega	float	Angular frequency of the oscillations (units: rad/s).	required
start_zero	bool	Determines if the charge begins oscillating at t=0. Defaults to False.	required
stop_t	Optional[float]	Time when the charge stops oscillating. If None, the charge never stops oscillating. Defaults to None.	required
q	float	Charge value, can be positive or negative. Default is e.	required

xacc(self, t)

Return x acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x acceleration at time values.

Source code in pycharge/charges.py

def xacc(self, t: Union[ndarray, float]) -> ndarray:
    xacc = -(self.direction[0]*self.amplitude
             * self.omega**2*np.cos(self.omega*t))
    if self.start_zero:
        xacc[t < 0] = 0
    if self.stop_t is not None:
        xacc[t > self.stop_t] = 0
    return xacc

xpos(self, t)

Return x position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x positions at time values.

Source code in pycharge/charges.py

def xpos(self, t: Union[ndarray, float]) -> ndarray:
    xpos = (self.direction[0]*self.amplitude*np.cos(self.omega*t)
            + self.origin[0])
    if self.start_zero:
        xpos[t < 0] = self.origin[0]
    if self.stop_t is not None:
        xpos[t > self.stop_t] = (self.direction[0]*self.amplitude
                                 * np.cos(self.omega*self.stop_t)
                                 + self.origin[0])
    return xpos

xvel(self, t)

Return x velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	x velocity at time values.

Source code in pycharge/charges.py

def xvel(self, t: Union[ndarray, float]) -> ndarray:
    xvel = -(self.direction[0]*self.amplitude
             * self.omega*np.sin(self.omega*t))
    if self.start_zero:
        xvel[t < 0] = 0
    if self.stop_t is not None:
        xvel[t > self.stop_t] = 0
    return xvel

yacc(self, t)

Return y acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	y acceleration at time values.

Source code in pycharge/charges.py

def yacc(self, t: Union[ndarray, float]) -> ndarray:
    yacc = -(self.direction[1]*self.amplitude
             * self.omega**2*np.cos(self.omega*t))
    if self.start_zero:
        yacc[t < 0] = 0
    if self.stop_t is not None:
        yacc[t > self.stop_t] = 0
    return yacc

ypos(self, t)

Return y position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	y position at time values.

Source code in pycharge/charges.py

def ypos(self, t: Union[ndarray, float]) -> ndarray:
    ypos = (self.direction[1]*self.amplitude*np.cos(self.omega*t)
            + self.origin[1])
    if self.start_zero:
        ypos[t < 0] = self.origin[1]
    if self.stop_t is not None:
        ypos[t > self.stop_t] = (self.direction[1]*self.amplitude
                                 * np.cos(self.omega*self.stop_t)
                                 + self.origin[1])
    return ypos

yvel(self, t)

Return y velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	y velocity at time values.

Source code in pycharge/charges.py

def yvel(self, t: Union[ndarray, float]) -> ndarray:
    yvel = -(self.direction[1]*self.amplitude
             * self.omega*np.sin(self.omega*t))
    if self.start_zero:
        yvel[t < 0] = 0
    if self.stop_t is not None:
        yvel[t > self.stop_t] = 0
    return yvel

zacc(self, t)

Return z acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	z acceleration at time values.

Source code in pycharge/charges.py

def zacc(self, t: Union[ndarray, float]) -> ndarray:
    zacc = -(self.direction[2]*self.amplitude
             * self.omega**2*np.cos(self.omega*t))
    if self.start_zero:
        zacc[t < 0] = 0
    if self.stop_t is not None:
        zacc[t > self.stop_t] = 0
    return zacc

zpos(self, t)

Return z position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	z position at time values.

Source code in pycharge/charges.py

def zpos(self, t: Union[ndarray, float]) -> ndarray:
    zpos = (self.direction[2]*self.amplitude*np.cos(self.omega*t)
            + self.origin[2])
    if self.start_zero:
        zpos[t < 0] = self.origin[2]
    if self.stop_t is not None:
        zpos[t > self.stop_t] = (self.direction[2]*self.amplitude
                                 * np.cos(self.omega*self.stop_t)
                                 + self.origin[2])
    return zpos

zvel(self, t)

Return z velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
ndarray	z velocity at time values.

Source code in pycharge/charges.py

def zvel(self, t: Union[ndarray, float]) -> ndarray:
    zvel = -(self.direction[2]*self.amplitude
             * self.omega*np.sin(self.omega*t))
    if self.start_zero:
        zvel[t < 0] = 0
    if self.stop_t is not None:
        zvel[t > self.stop_t] = 0
    return zvel

StationaryCharge

Stationary point charge.

Parameters:

Name	Type	Description	Default
position	Tuple[float, float, float]	List of x, y, and z values for the stationary position.	required
q	float	Charge value, can be positive or negative. Default is e.	required

xacc(self, t)

Return x acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	x acceleration at time values.

Source code in pycharge/charges.py

def xacc(self, t: Union[ndarray, float]) -> float:
    return 0

xpos(self, t)

Return x position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	x positions at time values.

Source code in pycharge/charges.py

def xpos(self, t: Union[ndarray, float]) -> float:
    return self.position[0]

xvel(self, t)

Return x velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	x velocity at time values.

Source code in pycharge/charges.py

def xvel(self, t: Union[ndarray, float]) -> float:
    return 0

yacc(self, t)

Return y acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	y acceleration at time values.

Source code in pycharge/charges.py

def yacc(self, t: Union[ndarray, float]) -> float:
    return 0

ypos(self, t)

Return y position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	y position at time values.

Source code in pycharge/charges.py

def ypos(self, t: Union[ndarray, float]) -> float:
    return self.position[1]

yvel(self, t)

Return y velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	y velocity at time values.

Source code in pycharge/charges.py

def yvel(self, t: Union[ndarray, float]) -> float:
    return 0

zacc(self, t)

Return z acceleration of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z acceleration at time values.

Source code in pycharge/charges.py

def zacc(self, t: Union[ndarray, float]) -> float:
    return 0

zpos(self, t)

Return z position of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z position at time values.

Source code in pycharge/charges.py

def zpos(self, t: Union[ndarray, float]) -> float:
    return self.position[2]

zvel(self, t)

Return z velocity of the charge at specified array of times.

Parameters:

Name	Type	Description	Default
t	Union[ndarray, float]	3D meshgrid array of time values.	required

Returns:

Type	Description
float	z velocity at time values.

Source code in pycharge/charges.py

def zvel(self, t: Union[ndarray, float]) -> float:
    return 0