div grad curl and all that

chapter 1 : Introduction, Vector Functions, and Electrostatics

Problem I-1

Using arrows of the proper magnitude and direction, sketch each of the following vector functions:

def plotvecfield(f):
    r = range(-3, 3, 1)
    s =0.5
    arrows = []
    for x10 in r:
        x = x10 * s
        for y10 in r:
            y = y10*s
            fx,fy = f(x,y)
            arrows.append(arrow((x,y), (x+fx, y+fy), hue=x*y))       
    sum(arrows).show(aspect_ratio=1)

a) iy + jx

def f(x,y):
    return (y,x)
    
plotvecfield(f)

b) (i + j) / √2

def f(x,y):
    return (x/sqrt(2), y/sqrt(2))
    
plotvecfield(f)

c) ix - jy

def f(x,y):
    return (x,-y)
    
plotvecfield(f)

d) iy

def f(x,y):
    return(y,0)

plotvecfield(f)

e) jx

def f(x,y):
    return(0,x)

plotvecfield(f)

f) (iy + jx)/ √(x² + y²), (x,y) ≠(0,0)

def f(x,y):
    t = sqrt(x^2+y^2)
    return(y/t, x/t)

plotvecfield(f)

g) iy + jxy

def f(x,y):
    return(y,x*y)

plotvecfield(f)

h) i + jy

def f(x,y):
    return(1,y)

plotvecfield(f)

Problem I-2

Using arrows, sketch the electric field of a unit positive charge situated at the origin. [Note: You may simplify the problem by confining your sketch to one of the coordinate plane. Does it matter which plane you choose?]

def f(x,y):
    return(x^2,y^2)

plotvecfield(f)