Electric field

The vector field generated by collection of fixed electrical charges, as dictated by Coulomb's law. This function is mainly used to provide examples for visualizing vector fields with ggvfields.

Usage

efield(u, charge_positions, charges, k = 1, q_test = +1, log = FALSE)

efield_maker(
  charge_positions = rbind(c(-1, -1), c(1, 1)),
  charges = c(-1, +1),
  k = 1,
  q_test = +1,
  log = FALSE
)

Arguments

u

The position of the test charge.

charge_positions

The positions of the fixed charges generating the electric field. Defaulted in efield_maker().

charges

The charges of the points placed at the positions of charge_positions. Defaulted in efield_maker().

k

The constant of proportionality, defaulted to 1. See examples for a more rigorous use of physical constants.

q_test

The test charge, defaulted to +1.

log

Executes the transformation of the double log of the norm of the vectors.

Value

A vector containing the force felt by the test charge on account of the electric field.

See also

https://en.wikipedia.org/wiki/Coulomb%27s_law

Examples

if (FALSE) { # \dontrun{
# set a - charge at (-1,-1) and a + charge at (1,1)
charge_positions <- rbind(c(-1,-1), c(1,1))
charges <- c(-1, +1)


# calculate force on test charge (+1) at c(0,1), ignoring physical constants
efield(c(0,1), charge_positions, charges)


# efield_maker() simply wraps this function, defaulting to those charges
f <- efield_maker()
f(c(0,1))

ggplot() +
  geom_stream_field(fun = f, xlim = c(-2,2), ylim = c(-2,2)) +
  scale_color_viridis_c(trans = "log10")

# electric constant from https://en.wikipedia.org/wiki/Vacuum_permittivity
ep0 <- 8.854187818814e-12
k <- (4*pi*ep0)^-1
efield(c(0,1), charge_positions, charges, k)
} # }